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<Text-field style="Heading 1" layout="Heading 1">1. Overview</Text-field></Title><Presentation-Block>
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<Text-field style="Text" layout="Normal">In finance, an exotic option is an option which has features making it more complex than commonly traded vanilla options. Like the more general exotic derivatives they may have several triggers relating to determination of payoff. An exotic option may also include non-standard underlying instrument, developed for a particular client or for a particular market. Exotic options are more complex than options that trade on an exchange, and are generally traded over the counter (OTC).</Text-field>
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<Text-field style="Text" layout="Normal">The term &quot;exotic option&quot; was popularized by Mark Rubinstein's 1990 working paper (published 1992, with Eric Reiner) &quot;Exotic Options&quot;, with the term based either on exotic wagers in horse racing, or due to the use of international terms such as &quot;Asian option&quot;, suggesting the &quot;exotic Orient&quot;.</Text-field>
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<Text-field style="Text" layout="Normal">Journalist Brian Palmer used the &quot;successful $1 bet on the superfecta&quot; in the 2010 Kentucky Derby that &quot;paid a whopping $101,284.60&quot; as an example of the controversial high-risk, high-payout exotic bets that were observed by track-watchers since the 1970s in his article about why we use the term exotic for certain types of financial instrument. Palmer compared these horse racing bets to the controversial emerging exotic financial instruments that concerned then-chairman of the Federal Reserve Paul Volcker in 1980. He argued that just as the exotic wagers survived the media controversy so will the exotic options.</Text-field>
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<Text-field style="Text" layout="Normal">In 1987, Bankers Trust Mark Standish and David Spaughton, were in Tokyo on business when &quot;they developed the first commercially used pricing formula for options linked to the average price of crude oil.&quot; They called this exotic option, the Asian option, because they were in Asia.</Text-field>
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<Text-field style="Heading 1" layout="Heading 1">2. Bermudan Options</Text-field></Title>
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<Group view="presentation" hide-input="false" hide-output="true" inline-output="false" labelreference="L9417" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input>
<Text-field style="Text" layout="Normal">A type of exotic option that can be exercised only on predetermined dates, typically every month. Bermuda options are a combination of American and European options. American options are exercisable anytime between the purchase date and the date of expiration. European options, conversely, are exercisable only at the date of expiration. Bermuda options are exercisable at the date of expiration, and on certain specified dates that occur between the purchase date and the date of expiration. 
</Text-field>
</Input>
</Group></Presentation-Block><Presentation-Block>
<Group view="presentation" hide-input="false" hide-output="true" inline-output="false" labelreference="L9419" drawlabel="true">
<Input>
<Text-field style="Text" layout="Normal">We will use directly the commands created by Maple with the following sintaxis:

</Text-field>
<Text-field style="Calling Sequence" font_style_name="Calling Sequence" superscript="false" placeholder="false" executable="false" selection-placeholder="false" italic="true" size="12" bold="false" subscript="false" family="Times New Roman" opaque="false" underline="false" background="[255,255,255]" readonly="false" foreground="[0,0,0]" layout="Normal">BermudanOption(<Font font_style_name="Help Maple Name" superscript="false" placeholder="false" executable="false" selection-placeholder="false" italic="true" size="12" bold="false" style="Help Maple Name" subscript="false" family="Times New Roman" opaque="false" underline="false" background="[255,255,255]" readonly="false" foreground="[0,0,0]">payoff</Font>, <Font font_style_name="Help Maple Name" superscript="false" placeholder="false" executable="false" selection-placeholder="false" italic="true" size="12" bold="false" style="Help Maple Name" subscript="false" family="Times New Roman" opaque="false" underline="false" background="[255,255,255]" readonly="false" foreground="[0,0,0]">exercisetimes</Font>, <Font font_style_name="Help Maple Name" superscript="false" placeholder="false" executable="false" selection-placeholder="false" italic="true" size="12" bold="false" style="Help Maple Name" subscript="false" family="Times New Roman" opaque="false" underline="false" background="[255,255,255]" readonly="false" foreground="[0,0,0]">opts</Font>)</Text-field>
<Text-field style="Calling Sequence" font_style_name="Calling Sequence" superscript="false" placeholder="false" executable="false" selection-placeholder="false" italic="true" size="12" bold="false" subscript="false" family="Times New Roman" opaque="false" underline="false" background="[255,255,255]" readonly="false" foreground="[0,0,0]" layout="Normal">BermudanOption(<Font font_style_name="Help Maple Name" superscript="false" placeholder="false" executable="false" selection-placeholder="false" italic="true" size="12" bold="false" style="Help Maple Name" subscript="false" family="Times New Roman" opaque="false" underline="false" background="[255,255,255]" readonly="false" foreground="[0,0,0]">payoff</Font>, <Font font_style_name="Help Maple Name" superscript="false" placeholder="false" executable="false" selection-placeholder="false" italic="true" size="12" bold="false" style="Help Maple Name" subscript="false" family="Times New Roman" opaque="false" underline="false" background="[255,255,255]" readonly="false" foreground="[0,0,0]">exercisedates</Font>, <Font font_style_name="Help Maple Name" superscript="false" placeholder="false" executable="false" selection-placeholder="false" italic="true" size="12" bold="false" style="Help Maple Name" subscript="false" family="Times New Roman" opaque="false" underline="false" background="[255,255,255]" readonly="false" foreground="[0,0,0]">opts</Font>)</Text-field>
<Text-field style="Text" layout="Normal"></Text-field>
</Input>
</Group></Presentation-Block><Table interior="group" showinput="true" alignment="left" exterior="none" width="100%" labelreference="L9423" showlabel="true" captionalignment="0" order="row" drawcaption="false" randomized="false" captionposition="1" plotalignlists="" pagebreak="cell" postexecute="insert" showgroup="true"><Table-Column weight="133" separator="false"></Table-Column><Table-Column weight="25" separator="false"></Table-Column><Table-Column weight="592" separator="false"></Table-Column><Table-Row align="baseline" separator="false"><Table-Cell columnspan="1" backgroundstyle="0" rowspan="1" padding="5" fillcolor="[255,255,255]">
<Text-field style="Text" layout="Normal"><Font font_style_name="Help Fixed" superscript="false" placeholder="false" executable="false" selection-placeholder="false" italic="false" size="12" bold="false" style="Help Fixed" subscript="false" family="Times New Roman" opaque="false" underline="false" background="[255,255,255]" readonly="false" foreground="[0,0,0]">payoff</Font></Text-field></Table-Cell><Table-Cell columnspan="1" backgroundstyle="0" rowspan="1" padding="5" fillcolor="[255,255,255]">
<Text-field style="Text" layout="Normal"><Font font_style_name="Help Fixed" superscript="false" placeholder="false" executable="false" selection-placeholder="false" italic="false" size="12" bold="false" style="Help Fixed" subscript="false" family="Times New Roman" opaque="false" underline="false" background="[255,255,255]" readonly="false" foreground="[0,0,0]">-</Font></Text-field></Table-Cell><Table-Cell columnspan="1" backgroundstyle="0" rowspan="1" padding="5" fillcolor="[255,255,255]">
<Text-field style="Text" layout="Normal">payoff function</Text-field></Table-Cell></Table-Row><Table-Row align="baseline" separator="false"><Table-Cell columnspan="1" backgroundstyle="0" rowspan="1" padding="5" fillcolor="[255,255,255]">
<Text-field style="Text" layout="Normal"><Font font_style_name="Help Fixed" superscript="false" placeholder="false" executable="false" selection-placeholder="false" italic="false" size="12" bold="false" style="Help Fixed" subscript="false" family="Times New Roman" opaque="false" underline="false" background="[255,255,255]" readonly="false" foreground="[0,0,0]">exercisedates</Font></Text-field></Table-Cell><Table-Cell columnspan="1" backgroundstyle="0" rowspan="1" padding="5" fillcolor="[255,255,255]">
<Text-field style="Text" layout="Normal"><Font font_style_name="Help Fixed" superscript="false" placeholder="false" executable="false" selection-placeholder="false" italic="false" size="12" bold="false" style="Help Fixed" subscript="false" family="Times New Roman" opaque="false" underline="false" background="[255,255,255]" readonly="false" foreground="[0,0,0]">-</Font></Text-field></Table-Cell><Table-Cell columnspan="1" backgroundstyle="0" rowspan="1" padding="5" fillcolor="[255,255,255]">
<Text-field style="Text" layout="Normal">list of dates given in a format recognized by ParseDate or a date data structure; dates when the option can be exercised</Text-field></Table-Cell></Table-Row><Table-Row align="baseline" separator="false"><Table-Cell columnspan="1" backgroundstyle="0" rowspan="1" padding="5" fillcolor="[255,255,255]">
<Text-field style="Text" layout="Normal"><Font font_style_name="Help Fixed" superscript="false" placeholder="false" executable="false" selection-placeholder="false" italic="false" size="12" bold="false" style="Help Fixed" subscript="false" family="Times New Roman" opaque="false" underline="false" background="[255,255,255]" readonly="false" foreground="[0,0,0]">exercisetimes</Font></Text-field></Table-Cell><Table-Cell columnspan="1" backgroundstyle="0" rowspan="1" padding="5" fillcolor="[255,255,255]">
<Text-field style="Text" layout="Normal"><Font font_style_name="Help Fixed" superscript="false" placeholder="false" executable="false" selection-placeholder="false" italic="false" size="12" bold="false" style="Help Fixed" subscript="false" family="Times New Roman" opaque="false" underline="false" background="[255,255,255]" readonly="false" foreground="[0,0,0]">-</Font></Text-field></Table-Cell><Table-Cell columnspan="1" backgroundstyle="0" rowspan="1" padding="5" fillcolor="[255,255,255]">
<Text-field style="Text" layout="Normal">list of non-negative constants; times when the option can be exercised</Text-field></Table-Cell></Table-Row><Table-Row align="baseline" separator="false"><Table-Cell columnspan="1" backgroundstyle="0" rowspan="1" padding="5" fillcolor="[255,255,255]">
<Text-field style="Text" layout="Normal"><Font font_style_name="Help Fixed" superscript="false" placeholder="false" executable="false" selection-placeholder="false" italic="false" size="12" bold="false" style="Help Fixed" subscript="false" family="Times New Roman" opaque="false" underline="false" background="[255,255,255]" readonly="false" foreground="[0,0,0]">opts</Font></Text-field></Table-Cell><Table-Cell columnspan="1" backgroundstyle="0" rowspan="1" padding="5" fillcolor="[255,255,255]">
<Text-field style="Text" layout="Normal"><Font font_style_name="Help Fixed" superscript="false" placeholder="false" executable="false" selection-placeholder="false" italic="false" size="12" bold="false" style="Help Fixed" subscript="false" family="Times New Roman" opaque="false" underline="false" background="[255,255,255]" readonly="false" foreground="[0,0,0]">-</Font></Text-field></Table-Cell><Table-Cell columnspan="1" backgroundstyle="0" rowspan="1" padding="5" fillcolor="[255,255,255]">
<Text-field style="Text" layout="Normal">(optional) equation(s) of the form <Font font_style_name="Help Maple Name" superscript="false" placeholder="false" executable="false" selection-placeholder="false" italic="false" size="12" bold="false" style="Help Maple Name" subscript="false" family="Times New Roman" opaque="false" underline="false" background="[255,255,255]" readonly="false" foreground="[0,0,0]">option</Font> = <Font font_style_name="Help Maple Name" superscript="false" placeholder="false" executable="false" selection-placeholder="false" italic="false" size="12" bold="false" style="Help Maple Name" subscript="false" family="Times New Roman" opaque="false" underline="false" background="[255,255,255]" readonly="false" foreground="[0,0,0]">value</Font> where <Font font_style_name="Help Maple Name" superscript="false" placeholder="false" executable="false" selection-placeholder="false" italic="false" size="12" bold="false" style="Help Maple Name" subscript="false" family="Times New Roman" opaque="false" underline="false" background="[255,255,255]" readonly="false" foreground="[0,0,0]">option</Font> is one of <Font font_style_name="Help Maple Name" superscript="false" placeholder="false" executable="false" selection-placeholder="false" italic="false" size="12" bold="false" style="Help Maple Name" subscript="false" family="Times New Roman" opaque="false" underline="false" background="[255,255,255]" readonly="false" foreground="[0,0,0]">referencedate</Font> or <Font font_style_name="Help Maple Name" superscript="false" placeholder="false" executable="false" selection-placeholder="false" italic="false" size="12" bold="false" style="Help Maple Name" subscript="false" family="Times New Roman" opaque="false" underline="false" background="[255,255,255]" readonly="false" foreground="[0,0,0]">daycounter</Font>; specify options for the <Font font_style_name="Help Maple Name" superscript="false" placeholder="false" executable="false" selection-placeholder="false" italic="false" size="12" bold="false" style="Help Maple Name" subscript="false" family="Times New Roman" opaque="false" underline="false" background="[255,255,255]" readonly="false" foreground="[0,0,0]">BermudanOption</Font> command</Text-field></Table-Cell></Table-Row></Table><Presentation-Block>
<Group view="presentation" hide-input="false" hide-output="true" inline-output="false" labelreference="L9422" drawlabel="true">
<Input>
<Text-field style="Text" layout="Bullet Item">The <Font font_style_name="Help Maple Name" superscript="false" placeholder="false" executable="false" selection-placeholder="false" italic="false" size="12" bold="false" style="Help Maple Name" subscript="false" family="Times New Roman" opaque="false" underline="false" background="[255,255,255]" readonly="false" foreground="[0,0,0]">BermudanOption</Font> command creates a new Bermudan-style option with the specified payoff and maturity. This option can be exercised at any time or date given in the <Font font_style_name="Help Maple Name" superscript="false" placeholder="false" executable="false" selection-placeholder="false" italic="false" size="12" bold="false" style="Help Maple Name" subscript="false" family="Times New Roman" opaque="false" underline="false" background="[255,255,255]" readonly="false" foreground="[0,0,0]">exercisetimes</Font> or <Font font_style_name="Help Maple Name" superscript="false" placeholder="false" executable="false" selection-placeholder="false" italic="false" size="12" bold="false" style="Help Maple Name" subscript="false" family="Times New Roman" opaque="false" underline="false" background="[255,255,255]" readonly="false" foreground="[0,0,0]">exercisedates</Font> list.</Text-field>
<Text-field style="Text" layout="Bullet Item">The parameter <Font font_style_name="Help Maple Name" superscript="false" placeholder="false" executable="false" selection-placeholder="false" italic="false" size="12" bold="false" style="Help Maple Name" subscript="false" family="Times New Roman" opaque="false" underline="false" background="[255,255,255]" readonly="false" foreground="[0,0,0]">payoff</Font> is the payoff function for the option. It can be either an algebraic expression or a procedure. A procedure defining a payoff function must accept one parameter (the value of the underlying) and return the corresponding payoff. This procedure will be called with floating-point arguments only and must return floating-point values. If <Font font_style_name="Help Maple Name" superscript="false" placeholder="false" executable="false" selection-placeholder="false" italic="false" size="12" bold="false" style="Help Maple Name" subscript="false" family="Times New Roman" opaque="false" underline="false" background="[255,255,255]" readonly="false" foreground="[0,0,0]">payoff</Font> is given as an algebraic expression it must depend on a single variable. This expression will be converted to a Maple procedure using the <Hyperlink linktarget="Help:unapply" hyperlink="true"><Font style="Hyperlink">unapply</Font></Hyperlink> function.</Text-field>
<Text-field style="Text" layout="Bullet Item">The parameter <Font font_style_name="Help Maple Name" superscript="false" placeholder="false" executable="false" selection-placeholder="false" italic="false" size="12" bold="false" style="Help Maple Name" subscript="false" family="Times New Roman" opaque="false" underline="false" background="[255,255,255]" readonly="false" foreground="[0,0,0]">exercisedates</Font> specifies the dates when the option can be exercised. It has to be given as a list of dates in any of the formats recognized by the <Hyperlink linktarget="Help:Finance[ParseDate]" hyperlink="true"><Font style="Hyperlink">ParseDate</Font></Hyperlink> command. The exercise times will be computed by converting the period between <Font font_style_name="Help Maple Name" superscript="false" placeholder="false" executable="false" selection-placeholder="false" italic="false" size="12" bold="false" style="Help Maple Name" subscript="false" family="Times New Roman" opaque="false" underline="false" background="[255,255,255]" readonly="false" foreground="[0,0,0]">referencedate</Font> and the corresponding exercise date to a fraction of the year according to the day count convention specified by <Font font_style_name="Help Maple Name" superscript="false" placeholder="false" executable="false" selection-placeholder="false" italic="false" size="12" bold="false" style="Help Maple Name" subscript="false" family="Times New Roman" opaque="false" underline="false" background="[255,255,255]" readonly="false" foreground="[0,0,0]">daycounter</Font>.</Text-field>
<Text-field style="Text" layout="Bullet Item">The LatticePrice command can be used to price a Bermudan-style option using any given binomial or trinomial tree.</Text-field>
<Text-field style="Text" layout="Normal"></Text-field>
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</Group></Presentation-Block><Presentation-Block>
<Group view="presentation" hide-input="false" hide-output="true" inline-output="false" labelreference="L9420" drawlabel="true">
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<Text-field style="Text" layout="Bullet Item" bullet="none">In the following section we will build a component that can be used to calculate directly the Bermudan Option.</Text-field>
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</Group></Presentation-Block><Presentation-Block>
<Group view="presentation" hide-input="false" hide-output="true" inline-output="false" labelreference="L9421" drawlabel="true">
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<Text-field style="Text" layout="Bullet Item" bullet="none">The interest reader can explore the command sequence of the action buttons.</Text-field>
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</Group></Presentation-Block></Table-Cell></Table-Row></Table><Presentation-Block>
<Group view="presentation" hide-input="false" hide-output="true" inline-output="false" labelreference="L1940" drawlabel="true">
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<Text-field style="Text" layout="Normal"></Text-field>
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</Group></Presentation-Block>
</Section>
<Section collapsed="true" MultipleChoiceAnswerIndex="-1" MultipleChoiceRandomizeChoices="false" TrueFalseAnswerIndex="-1" EssayAnswerRows="5" EssayAnswerColumns="60"><Title>
<Text-field style="Heading 2" layout="Heading 2">2.2 Maple Component for Bermudan Options</Text-field></Title><Presentation-Block>
<Group view="presentation" hide-input="false" hide-output="true" inline-output="false" labelreference="L1934" drawlabel="true">
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<Text-field style="Text" layout="Normal"><Equation executable="false" style="2D Math" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2I1EhRicvJSxtYXRodmFyaWFudEdRJ25vcm1hbEYn">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=</Equation><Equation executable="false" style="2D Math" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2I1EhRicvJSxtYXRodmFyaWFudEdRJ25vcm1hbEYn">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=</Equation><Equation executable="true" style="2D Input" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2I1EhRicvJStleGVjdXRhYmxlR1EmZmFsc2VGJy8lLG1hdGh2YXJpYW50R1Enbm9ybWFsRic=">JSFH</Equation></Text-field>
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</Group></Presentation-Block><Presentation-Block><CodeEditor-ExecGroup view="presentation" hide-input="false" hide-output="true" inline-output="false" labelreference="L5" display="code"><EC-CodeEditor id="CodeEditRegion0" visible="false" pixel-width="500" pixel-height="200" code-language="text/maple" autoexpand="true" wrapping="false" show-border="true" code-line-numbers="true"># RESTART AND LOAD PACKAGES
restart:
with(Finance):
with(plots):</EC-CodeEditor></CodeEditor-ExecGroup></Presentation-Block><Table interior="group" showinput="true" alignment="left" exterior="all" width="76.33517495395948%" labelreference="L1950" showlabel="true" captionalignment="0" title="" order="row" drawcaption="false" randomized="false" captionposition="1" plotalignlists="" pagebreak="cell" postexecute="insert" showgroup="true"><Table-Column weight="386" separator="true"></Table-Column><Table-Column weight="443" separator="true"></Table-Column><Table-Row align="top" separator="true"><Table-Cell columnspan="1" backgroundstyle="1" rowspan="1" padding="5" fillcolor="[204,255,255]"><Presentation-Block>
<Group view="presentation" hide-input="false" hide-output="true" inline-output="false" labelreference="L1951" drawlabel="true">
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<Text-field style="Text" layout="Normal" alignment="centred"><Font bold="true">Calendar and Pay off funnction</Font></Text-field>
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</Group></Presentation-Block></Table-Cell><Table-Cell columnspan="1" backgroundstyle="1" rowspan="1" padding="5" fillcolor="[204,255,255]"><Presentation-Block>
<Group view="presentation" hide-input="false" hide-output="true" inline-output="false" labelreference="L1952" drawlabel="true">
<Input>
<Text-field style="Text" layout="Normal" alignment="centred"><Font bold="true">Plot Pay off function</Font></Text-field>
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</Group></Presentation-Block></Table-Cell></Table-Row><Table-Row align="top" separator="true"><Table-Cell columnspan="1" backgroundstyle="0" rowspan="1" padding="5" fillcolor="[255,255,255]"><Presentation-Block>
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<Group view="presentation" hide-input="false" hide-output="true" inline-output="false" labelreference="L1954" drawlabel="true">
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<Text-field style="Text" italic="true" layout="Normal" alignment="centred"><Font italic="true">Fraction of Year Calculator</Font></Text-field>
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</Group></Presentation-Block><Presentation-Block>
<Group view="presentation" hide-input="false" hide-output="true" inline-output="false" labelreference="L2052" drawlabel="true">
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<Text-field style="Text" italic="true" layout="Normal" alignment="centred"></Text-field>
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<Group view="presentation" hide-input="false" hide-output="true" inline-output="false" labelreference="L1992" drawlabel="true">
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<Text-field style="Text" italic="true" layout="Normal" alignment="centred"><Font italic="true">Evaluation date</Font></Text-field>
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<Group view="presentation" hide-input="false" hide-output="true" inline-output="false" labelreference="L1987" drawlabel="true">
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<Text-field style="Text" layout="Normal" alignment="centred">     <EC-TextArea id="TextArea22" enabled="true" visible="true" visiblecharacterwidth="18" visiblerows="1" contents="&quot;January-3-2014&quot;" editable="true" wrapping="true" show-border="true" password="false"></EC-TextArea></Text-field>
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<Group view="presentation" hide-input="false" hide-output="true" inline-output="false" labelreference="L1999" drawlabel="true">
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<Text-field style="Text" layout="Normal" alignment="centred"><Font italic="true">Calendar Convention</Font></Text-field>
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<Group view="presentation" hide-input="false" hide-output="true" inline-output="false" labelreference="L2048" drawlabel="true">
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<Text-field style="Text" layout="Normal" alignment="centred">
<EC-RadioButton id="RadioButton1" groupname="Group0" caption="ISMA" enabled="true" visible="true" selected="false"></EC-RadioButton><EC-RadioButton id="RadioButton2" groupname="Group0" caption="ISDA" enabled="true" visible="true" selected="false"></EC-RadioButton><EC-RadioButton id="RadioButton3" groupname="Group0" caption="360" enabled="true" visible="true" selected="false"></EC-RadioButton><EC-RadioButton id="RadioButton4" groupname="Group0" caption="365" enabled="true" visible="true" selected="false"></EC-RadioButton></Text-field>
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<Group view="presentation" hide-input="false" hide-output="true" inline-output="false" labelreference="L2086" drawlabel="true">
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<Text-field style="Text" layout="Normal" alignment="centred">
<Font italic="true">Exercise Date <EC-TextArea id="TextArea25" enabled="true" visible="true" visiblecharacterwidth="20" visiblerows="1" contents="&quot;June-10-2019&quot;" editable="true" wrapping="true" show-border="true" password="false"></EC-TextArea> </Font></Text-field>
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<Group view="presentation" hide-input="false" hide-output="true" inline-output="false" labelreference="L1978" drawlabel="true">
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<Text-field style="Text" italic="true" layout="Normal" alignment="centred"><Font italic="true">Fraction of Year <EC-MathContainer id="MathContainer9" pixel-width="200" pixel-height="40" expression="&lt;math xmlns='http://www.w3.org/1998/Math/MathML'&gt;&lt;mstyle fontfamily='Times New Roman' mathsize='12pt' mathcolor='#000000'  veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.7099999785423279' scriptminsize='8.0pt'&gt;&lt;mn fontweight='normal'&gt;5.416666667&lt;/mn&gt;&lt;/mstyle&gt;&lt;/math&gt;" visible="true" show-border="true" autofit="false"></EC-MathContainer></Font></Text-field>
</Input>
</Group></Presentation-Block><Presentation-Block>
<Group view="presentation" hide-input="false" hide-output="true" inline-output="false" labelreference="L1979" drawlabel="true">
<Input>
<Text-field style="Text" italic="true" layout="Normal" alignment="centred"></Text-field>
</Input>
</Group></Presentation-Block><Presentation-Block>
<Group view="presentation" hide-input="false" hide-output="true" inline-output="false" labelreference="L2091" drawlabel="true">
<Input>
<Text-field style="Text" layout="Normal" alignment="centred"></Text-field>
</Input>
</Group></Presentation-Block><Presentation-Block>
<Group view="presentation" hide-input="false" hide-output="true" inline-output="false" labelreference="L2092" drawlabel="true">
<Input>
<Text-field style="Text" layout="Normal" alignment="centred"></Text-field>
</Input>
</Group></Presentation-Block><Presentation-Block>
<Group view="presentation" hide-input="false" hide-output="true" inline-output="false" labelreference="L2055" drawlabel="true">
<Input>
<Text-field style="Text" italic="true" layout="Normal" alignment="centred"><EC-Button id="Button4" caption="Calculate Fraction of Year" pixel-width="300" pixel-height="200" enabled="true" visible="true" show-border="true" user-size="false"><MapleCode action="click-event-handler">use DocumentTools, Finance in 

Do(a=DocumentTools[GetProperty]('RadioButton1','value')):
Do(b=DocumentTools[GetProperty]('RadioButton2','value')):
Do(c=DocumentTools[GetProperty]('RadioButton3','value')):
Do(d=DocumentTools[GetProperty]('RadioButton4','value')):

if a=&quot;true&quot; then
	Do(f=1);
	elif b=&quot;true&quot; then 
	Do(f=2);
	elif c=&quot;true&quot; then
	Do(f=3);
	elif d=&quot;true&quot; then 
	Do(f=4);
end if;
		
if f=1 then
	Do(h=Finance[DayCounter](Bond)):
	Do(Settings(daycounter=&quot;Bond&quot;)):
	elif f=2 then 
	Do(h=Finance[DayCounter](Actual365Fixed)):
	Do(Settings(daycounter=&quot;Actual365Fixed&quot;)):
	elif f=3 then
	Do(h=Finance[DayCounter](ISDA)):
	Do(Settings(daycounter=&quot;ISDA&quot;)):
	elif f=4 then 
	Do(h=Finance[DayCounter](Actual360)):
	Do(Settings(daycounter=&quot;Actual360&quot;)):
end if;

Do(fecha1= %TextArea22);  
Do(fecha2= %TextArea25); 

Do(%MathContainer9=YearFraction(fecha1,fecha2,h)):
Do(SetProperty(Button3,enabled,&quot;true&quot;)):
end use; 
</MapleCode></EC-Button></Text-field>
</Input>
</Group></Presentation-Block><Presentation-Block>
<Group view="presentation" hide-input="false" hide-output="true" inline-output="false" labelreference="L2057" drawlabel="true">
<Input>
<Text-field style="Text" italic="true" layout="Normal" alignment="centred"></Text-field>
</Input>
</Group></Presentation-Block><Presentation-Block>
<Group view="presentation" hide-input="false" hide-output="true" inline-output="false" labelreference="L2082" drawlabel="true">
<Input>
<Text-field style="Text" layout="Normal" alignment="centred"></Text-field>
</Input>
</Group></Presentation-Block><Presentation-Block>
<Group view="presentation" hide-input="false" hide-output="true" inline-output="false" labelreference="L2083" drawlabel="true">
<Input>
<Text-field style="Text" layout="Normal" alignment="centred"></Text-field>
</Input>
</Group></Presentation-Block><Presentation-Block>
<Group view="presentation" hide-input="false" hide-output="true" inline-output="false" labelreference="L2007" drawlabel="true">
<Input>
<Text-field style="Text" italic="true" layout="Normal" alignment="centred"><Font italic="true">Execution Dates counted in Fraction of Years</Font></Text-field>
</Input>
</Group></Presentation-Block><Presentation-Block>
<Group view="presentation" hide-input="false" hide-output="true" inline-output="false" labelreference="L2004" drawlabel="true">
<Input>
<Text-field style="Text" layout="Normal" alignment="centred"></Text-field>
</Input>
</Group></Presentation-Block><Presentation-Block>
<Group view="presentation" hide-input="false" hide-output="true" inline-output="false" labelreference="L2005" drawlabel="true">
<Input>
<Text-field style="Text" layout="Normal" alignment="centred"><EC-MathContainer id="MathContainer8" pixel-width="300" pixel-height="100" expression="&lt;math xmlns='http://www.w3.org/1998/Math/MathML'&gt;&lt;mstyle fontfamily='Times New Roman' mathsize='12pt' mathcolor='#000000'  veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.7099999785423279' scriptminsize='8.0pt'&gt;&lt;mrow&gt;&lt;mfenced open='[' close=']' separators=','&gt;&lt;mrow&gt;&lt;mn fontweight='normal'&gt;0.5&lt;/mn&gt;&lt;mo fontweight='normal' separator='true' lspace='0.0em' rspace='0.3333333em'&gt;&amp;comma;&lt;/mo&gt;&lt;mspace height='0.0ex' width='1.0em' depth='0.0ex' linebreak='nobreak'/&gt;&lt;mn fontweight='normal'&gt;1.0&lt;/mn&gt;&lt;mo fontweight='normal' separator='true' lspace='0.0em' rspace='0.3333333em'&gt;&amp;comma;&lt;/mo&gt;&lt;mspace height='0.0ex' width='1.0em' depth='0.0ex' linebreak='nobreak'/&gt;&lt;mn fontweight='normal'&gt;1.5&lt;/mn&gt;&lt;mo fontweight='normal' separator='true' lspace='0.0em' rspace='0.3333333em'&gt;&amp;comma;&lt;/mo&gt;&lt;mspace height='0.0ex' width='1.0em' depth='0.0ex' linebreak='nobreak'/&gt;&lt;mn fontweight='normal'&gt;2.0&lt;/mn&gt;&lt;/mrow&gt;&lt;/mfenced&gt;&lt;/mrow&gt;&lt;/mstyle&gt;&lt;/math&gt;" visible="true" show-border="true" autofit="false"></EC-MathContainer></Text-field>
</Input>
</Group></Presentation-Block><Presentation-Block>
<Group view="presentation" hide-input="false" hide-output="true" inline-output="false" labelreference="L2001" drawlabel="true">
<Input>
<Text-field style="Text" layout="Normal" alignment="centred"></Text-field>
</Input>
</Group></Presentation-Block><Presentation-Block>
<Group view="presentation" hide-input="false" hide-output="true" inline-output="false" labelreference="L2002" drawlabel="true">
<Input>
<Text-field style="Text" layout="Normal" alignment="centred"></Text-field>
</Input>
</Group></Presentation-Block><Presentation-Block>
<Group view="presentation" hide-input="false" hide-output="true" inline-output="false" labelreference="L1966" drawlabel="true">
<Input>
<Text-field style="Text" layout="Normal" alignment="centred"></Text-field>
</Input>
</Group></Presentation-Block></Table-Cell><Table-Cell columnspan="1" backgroundstyle="0" rowspan="1" padding="5" fillcolor="[255,255,255]"><Presentation-Block>
<Group view="presentation" hide-input="false" hide-output="true" inline-output="false" labelreference="L2015" drawlabel="true">
<Input>
<Text-field style="Text" layout="Normal" alignment="centred"><Equation executable="false" style="2D Math" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2I1EhRicvJSxtYXRodmFyaWFudEdRJ25vcm1hbEYn">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=</Equation></Text-field>
</Input>
</Group></Presentation-Block><Presentation-Block>
<Group view="presentation" hide-input="false" hide-output="true" inline-output="false" labelreference="L2059" drawlabel="true">
<Input>
<Text-field style="Text" layout="Normal" alignment="centred"><Equation executable="false" style="2D Math" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2I1EhRicvJSxtYXRodmFyaWFudEdRJ25vcm1hbEYn">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=</Equation></Text-field>
</Input>
</Group></Presentation-Block><Presentation-Block>
<Group view="presentation" hide-input="false" hide-output="true" inline-output="false" labelreference="L2017" drawlabel="true">
<Input>
<Text-field style="Text" layout="Normal" alignment="centred"></Text-field>
</Input>
</Group></Presentation-Block><Presentation-Block>
<Group view="presentation" hide-input="false" hide-output="true" inline-output="false" labelreference="L1955" drawlabel="true">
<Input>
<Text-field style="Text" layout="Normal" alignment="centred"><EC-Plot id="Plot3" visible="true" pixel-width="400" pixel-height="400" continuous="false" delay="100" clickx="1.7976931348623157E308" clicky="1.7976931348623157E308" startx="0.0" starty="0.0" endx="0.0" endy="0.0" clickdefault="false" labelreference="L1968" drawcaption="false" captionposition="1" captionalignment="0" show-border="true"><Plot height="400.0" type="two-dimensional" width="400.0" plot-scale="1.0" plot-xtrans="0.0" plot-ytrans="0.0" gridlinevisibility="7" 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</Input>
</Group></Presentation-Block><Presentation-Block>
<Group view="presentation" hide-input="false" hide-output="true" inline-output="false" labelreference="L2027" drawlabel="true">
<Input>
<Text-field style="Text" layout="Normal" alignment="centred"></Text-field>
</Input>
</Group></Presentation-Block><Presentation-Block>
<Group view="presentation" hide-input="false" hide-output="true" inline-output="false" labelreference="L2065" drawlabel="true">
<Input>
<Text-field style="Text" layout="Normal" alignment="centred">Pay off Function</Text-field>
</Input>
</Group></Presentation-Block><Presentation-Block>
<Group view="presentation" hide-input="false" hide-output="true" inline-output="false" labelreference="L2066" drawlabel="true">
<Input>
<Text-field style="Text" layout="Normal" alignment="centred"><EC-MathContainer id="MathContainer7" pixel-width="350" pixel-height="100" expression="&lt;math xmlns='http://www.w3.org/1998/Math/MathML'&gt;&lt;mstyle fontfamily='Times New Roman' mathsize='12pt' mathcolor='#000000'  veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.7099999785423279' scriptminsize='8.0pt'&gt;&lt;mrow&gt;&lt;mrow&gt;&lt;mrow&gt;&lt;mrow&gt;&lt;mi fontweight='normal'&gt;piecewise&lt;/mi&gt;&lt;mo fontweight='normal' lspace='0.0em' rspace='0.0em'&gt;&amp;ApplyFunction;&lt;/mo&gt;&lt;mfenced open='(' close=')' separators=','&gt;&lt;mrow&gt;&lt;mrow&gt;&lt;mi fontweight='normal'&gt;S&lt;/mi&gt;&lt;mo fontweight='normal' lspace='0.2777778em' rspace='0.2777778em'&gt;&amp;lt;&lt;/mo&gt;&lt;mn fontweight='normal'&gt;90&lt;/mn&gt;&lt;/mrow&gt;&lt;mo fontweight='normal' separator='true' lspace='0.0em' rspace='0.3333333em'&gt;&amp;comma;&lt;/mo&gt;&lt;mn fontweight='normal'&gt;0&lt;/mn&gt;&lt;mo fontweight='normal' separator='true' lspace='0.0em' rspace='0.3333333em'&gt;&amp;comma;&lt;/mo&gt;&lt;mrow&gt;&lt;mi fontweight='normal'&gt;S&lt;/mi&gt;&lt;mo fontweight='normal' lspace='0.2777778em' rspace='0.2777778em'&gt;&amp;lt;&lt;/mo&gt;&lt;mn fontweight='normal'&gt;100&lt;/mn&gt;&lt;/mrow&gt;&lt;mo fontweight='normal' separator='true' lspace='0.0em' rspace='0.3333333em'&gt;&amp;comma;&lt;/mo&gt;&lt;mrow&gt;&lt;mi fontweight='normal'&gt;S&lt;/mi&gt;&lt;mo fontweight='normal' lspace='0.2222222em' rspace='0.2222222em'&gt;&amp;minus;&lt;/mo&gt;&lt;mn fontweight='normal'&gt;90&lt;/mn&gt;&lt;/mrow&gt;&lt;mo fontweight='normal' separator='true' lspace='0.0em' rspace='0.3333333em'&gt;&amp;comma;&lt;/mo&gt;&lt;mrow&gt;&lt;mi fontweight='normal'&gt;S&lt;/mi&gt;&lt;mo fontweight='normal' lspace='0.2777778em' rspace='0.2777778em'&gt;&amp;lt;&lt;/mo&gt;&lt;mn fontweight='normal'&gt;110&lt;/mn&gt;&lt;/mrow&gt;&lt;mo fontweight='normal' separator='true' lspace='0.0em' rspace='0.3333333em'&gt;&amp;comma;&lt;/mo&gt;&lt;mrow&gt;&lt;mn fontweight='normal'&gt;110&lt;/mn&gt;&lt;mo fontweight='normal' lspace='0.2222222em' rspace='0.2222222em'&gt;&amp;minus;&lt;/mo&gt;&lt;mi fontweight='normal'&gt;S&lt;/mi&gt;&lt;/mrow&gt;&lt;mo fontweight='normal' separator='true' lspace='0.0em' rspace='0.3333333em'&gt;&amp;comma;&lt;/mo&gt;&lt;mn fontweight='normal'&gt;0&lt;/mn&gt;&lt;/mrow&gt;&lt;/mfenced&gt;&lt;/mrow&gt;&lt;/mrow&gt;&lt;/mrow&gt;&lt;/mrow&gt;&lt;/mstyle&gt;&lt;/math&gt;" visible="true" show-border="true" autofit="false"></EC-MathContainer></Text-field>
</Input>
</Group></Presentation-Block><Presentation-Block>
<Group view="presentation" hide-input="false" hide-output="true" inline-output="false" labelreference="L2062" drawlabel="true">
<Input>
<Text-field style="Text" layout="Normal" alignment="centred"></Text-field>
</Input>
</Group></Presentation-Block><Presentation-Block>
<Group view="presentation" hide-input="false" hide-output="true" inline-output="false" labelreference="L2028" drawlabel="true">
<Input>
<Text-field style="Text" italic="true" layout="Normal" alignment="centred"><Font italic="true">plot range from <EC-TextArea id="TextArea23" enabled="true" visible="true" visiblecharacterwidth="10" visiblerows="1" contents="80" editable="true" wrapping="true" show-border="true" password="false"></EC-TextArea>to <EC-TextArea id="TextArea24" enabled="true" visible="true" visiblecharacterwidth="10" visiblerows="1" contents="120" editable="true" wrapping="true" show-border="true" password="false"></EC-TextArea></Font></Text-field>
</Input>
</Group></Presentation-Block><Presentation-Block>
<Group view="presentation" hide-input="false" hide-output="true" inline-output="false" labelreference="L2068" drawlabel="true">
<Input>
<Text-field style="Text" layout="Normal" alignment="centred"></Text-field>
</Input>
</Group></Presentation-Block><Presentation-Block>
<Group view="presentation" hide-input="false" hide-output="true" inline-output="false" labelreference="L2069" drawlabel="true">
<Input>
<Text-field style="Text" layout="Normal" alignment="centred"><EC-Button id="Button3" caption="Plot Pay off Function" pixel-width="300" pixel-height="200" enabled="true" visible="true" show-border="true" user-size="false"><MapleCode action="click-event-handler">use DocumentTools, Finance, plots, Statistics in 
#module()
Do(P1=unapply(%MathContainer7, S)):
Do(%Plot3=plot(P1, %TextArea23 .. %TextArea24, thickness = 2, axes = BOXED, gridlines = true, color = blue)):


Do(fecha1= %TextArea22);  

Do(a=DocumentTools[GetProperty]('RadioButton1','value')):
Do(b=DocumentTools[GetProperty]('RadioButton2','value')):
Do(c=DocumentTools[GetProperty]('RadioButton3','value')):
Do(d=DocumentTools[GetProperty]('RadioButton4','value')):


if a=&quot;true&quot; then
	Do(f=1);
	elif b=&quot;true&quot; then 
	Do(f=2);
	elif c=&quot;true&quot; then
	Do(f=3);
	elif d=&quot;true&quot; then 
	Do(f=4);
end if;
		
if f=1 then
	Do(h=Finance[DayCounter](Bond)):
	elif f=2 then 
	Do(h=Finance[DayCounter](Actual365Fixed)):
	elif f=3 then
	Do(h=Finance[DayCounter](ISDA)):
	elif f=4 then 
	Do(h=Finance[DayCounter](Actual360)):
end if;

Do(Settings(daycounter=h));
Do(SetProperty(Button5, enabled, &quot;true&quot;)):
#end module;
end use; 
</MapleCode></EC-Button></Text-field>
</Input>
</Group></Presentation-Block><Presentation-Block>
<Group view="presentation" hide-input="false" hide-output="true" inline-output="false" labelreference="L2029" drawlabel="true">
<Input>
<Text-field style="Text" layout="Normal" alignment="centred"></Text-field>
</Input>
</Group></Presentation-Block></Table-Cell></Table-Row></Table><Presentation-Block>
<Group view="presentation" hide-input="false" hide-output="true" inline-output="false" labelreference="L1946" drawlabel="true">
<Input>
<Text-field style="Text" layout="Normal"><Equation executable="false" style="2D Math" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2I1EhRicvJSxtYXRodmFyaWFudEdRJ25vcm1hbEYn">JSFH</Equation></Text-field>
</Input>
</Group></Presentation-Block><Table interior="none" showinput="true" alignment="left" exterior="all" width="76.42725%" labelreference="L2094" showlabel="true" captionalignment="0" title="" drawtitle="false" order="row" drawcaption="false" randomized="false" captionposition="1" plotalignlists="" pagebreak="cell" postexecute="insert" showgroup="true"><Table-Column weight="386" separator="true"></Table-Column><Table-Column weight="444" separator="true"></Table-Column><Table-Row align="top" separator="true"><Table-Cell columnspan="1" backgroundstyle="0" rowspan="1" padding="5" fillcolor="[255,255,255]"><Presentation-Block>
<Group view="presentation" hide-input="false" hide-output="true" inline-output="false" labelreference="L2139" drawlabel="true">
<Input>
<Text-field style="Text" italic="true" layout="Normal" alignment="centred"></Text-field>
</Input>
</Group></Presentation-Block><Presentation-Block>
<Group view="presentation" hide-input="false" hide-output="true" inline-output="false" labelreference="L2128" drawlabel="true">
<Input>
<Text-field style="Text" italic="true" layout="Normal" alignment="centred"><Font italic="true">Parameters of the </Font></Text-field>
</Input>
</Group></Presentation-Block><Presentation-Block>
<Group view="presentation" hide-input="false" hide-output="true" inline-output="false" labelreference="L2124" drawlabel="true">
<Input>
<Text-field style="Text" italic="true" layout="Normal" alignment="centred"><Font italic="true">Black-Scholes Binomial Tree</Font></Text-field>
</Input>
</Group></Presentation-Block><Presentation-Block>
<Group view="presentation" hide-input="false" hide-output="true" inline-output="false" labelreference="L2136" drawlabel="true">
<Input>
<Text-field style="Text" italic="true" size="10" layout="Normal" alignment="centred"></Text-field>
</Input>
</Group></Presentation-Block><Presentation-Block>
<Group view="presentation" hide-input="false" hide-output="true" inline-output="false" labelreference="L2137" drawlabel="true">
<Input>
<Text-field style="Text" italic="true" size="10" layout="Normal" alignment="centred"><Font italic="true" size="10">S0</Font></Text-field>
</Input>
</Group></Presentation-Block><Presentation-Block>
<Group view="presentation" hide-input="false" hide-output="true" inline-output="false" labelreference="L9441" drawlabel="true">
<Input>
<Text-field style="Text" italic="true" size="10" layout="Normal" alignment="centred"><EC-TextArea id="TextArea26" enabled="true" visible="true" visiblecharacterwidth="10" visiblerows="1" contents="100" editable="true" wrapping="true" show-border="true" password="false"></EC-TextArea></Text-field>
</Input>
</Group></Presentation-Block><Presentation-Block>
<Group view="presentation" hide-input="false" hide-output="true" inline-output="false" labelreference="L2122" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input>
<Text-field style="Text" italic="true" size="10" layout="Normal" alignment="centred"><Font italic="true" size="10">r</Font></Text-field>
</Input>
</Group></Presentation-Block><Presentation-Block>
<Group view="presentation" hide-input="false" hide-output="true" inline-output="false" labelreference="L9443" drawlabel="true">
<Input>
<Text-field style="Text" italic="true" size="10" layout="Normal" alignment="centred"><EC-TextArea id="TextArea27" enabled="true" visible="true" visiblecharacterwidth="10" visiblerows="1" contents="0.1" editable="true" wrapping="true" show-border="true" password="false"></EC-TextArea><Font italic="true" size="10"> </Font></Text-field>
</Input>
</Group></Presentation-Block><Presentation-Block>
<Group view="presentation" hide-input="false" hide-output="true" inline-output="false" labelreference="L2108" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input>
<Text-field style="Text" italic="true" size="10" layout="Normal" alignment="centred"><Font encoding="UTF-8" italic="true" size="10">\317\203</Font></Text-field>
</Input>
</Group></Presentation-Block><Presentation-Block>
<Group view="presentation" hide-input="false" hide-output="true" inline-output="false" labelreference="L9449" drawlabel="true">
<Input>
<Text-field style="Text" italic="true" size="10" layout="Normal" alignment="centred"><EC-TextArea id="TextArea28" enabled="true" visible="true" visiblecharacterwidth="10" visiblerows="1" contents="0.40" editable="true" wrapping="true" show-border="true" password="false"></EC-TextArea><Font italic="true" size="10"> </Font></Text-field>
</Input>
</Group></Presentation-Block><Presentation-Block>
<Group view="presentation" hide-input="false" hide-output="true" inline-output="false" labelreference="L9445" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input>
<Text-field style="Text" italic="true" size="10" layout="Normal" alignment="centred"><Font italic="true" size="10">d</Font></Text-field>
</Input>
</Group></Presentation-Block><Presentation-Block>
<Group view="presentation" hide-input="false" hide-output="true" inline-output="false" labelreference="L9451" drawlabel="true">
<Input>
<Text-field style="Text" italic="true" size="10" layout="Normal" alignment="centred"><EC-TextArea id="TextArea29" enabled="true" visible="true" visiblecharacterwidth="10" visiblerows="1" contents="0.1" editable="true" wrapping="true" show-border="true" password="false"></EC-TextArea><Font italic="true" size="10"> </Font></Text-field>
</Input>
</Group></Presentation-Block><Presentation-Block>
<Group view="presentation" hide-input="false" hide-output="true" inline-output="false" labelreference="L9453" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input>
<Text-field style="Text" italic="true" size="10" layout="Normal" alignment="centred"><Font italic="true" size="10">T
<EC-TextArea id="TextArea30" enabled="true" visible="true" visiblecharacterwidth="10" visiblerows="1" contents="3" editable="true" wrapping="true" show-border="true" password="false"></EC-TextArea> </Font></Text-field>
</Input>
</Group></Presentation-Block><Presentation-Block>
<Group view="presentation" hide-input="false" hide-output="true" inline-output="false" labelreference="L2114" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input>
<Text-field style="Text" italic="true" size="10" layout="Normal" alignment="centred"><Font italic="true" size="10">N (computation)</Font></Text-field>
</Input>
</Group></Presentation-Block><Presentation-Block>
<Group view="presentation" hide-input="false" hide-output="true" inline-output="false" labelreference="L9437" drawlabel="true">
<Input>
<Text-field style="Text" italic="true" size="10" layout="Normal" alignment="centred"><EC-TextArea id="TextArea32" enabled="true" visible="true" visiblecharacterwidth="10" visiblerows="1" contents="500" editable="true" wrapping="true" show-border="true" password="false"></EC-TextArea></Text-field>
</Input>
</Group></Presentation-Block><Presentation-Block>
<Group view="presentation" hide-input="false" hide-output="true" inline-output="false" labelreference="L2154" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input>
<Text-field style="Text" italic="true" size="10" layout="Normal" alignment="centred"><Font italic="true" size="10">N (graph)</Font></Text-field>
</Input>
</Group></Presentation-Block><Presentation-Block>
<Group view="presentation" hide-input="false" hide-output="true" inline-output="false" labelreference="L9439" drawlabel="true">
<Input>
<Text-field style="Text" italic="true" size="10" layout="Normal" alignment="centred"><EC-TextArea id="TextArea31" enabled="true" visible="true" visiblecharacterwidth="10" visiblerows="1" contents="20" editable="true" wrapping="true" show-border="true" password="false"></EC-TextArea><Font italic="true" size="10"> </Font></Text-field>
</Input>
</Group></Presentation-Block><Presentation-Block>
<Group view="presentation" hide-input="false" hide-output="true" inline-output="false" labelreference="L2117" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input>
<Text-field style="Text" italic="true" layout="Normal" alignment="centred"></Text-field>
</Input>
</Group></Presentation-Block><Presentation-Block>
<Group view="presentation" hide-input="false" hide-output="true" inline-output="false" labelreference="L2107" drawlabel="true">
<Input>
<Text-field style="Text" layout="Normal" alignment="centred"><Equation executable="false" style="2D Math" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2I1EhRicvJSxtYXRodmFyaWFudEdRJ25vcm1hbEYn">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=</Equation></Text-field>
</Input>
</Group></Presentation-Block><Presentation-Block>
<Group view="presentation" hide-input="false" hide-output="true" inline-output="false" labelreference="L2271" drawlabel="true">
<Input>
<Text-field style="Text" layout="Normal" alignment="centred"><Equation executable="false" style="2D Math" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2I1EhRicvJSxtYXRodmFyaWFudEdRJ25vcm1hbEYn">JSFH</Equation></Text-field>
</Input>
</Group></Presentation-Block><Presentation-Block>
<Group view="presentation" hide-input="false" hide-output="true" inline-output="false" labelreference="L2143" drawlabel="true">
<Input>
<Text-field style="Text" layout="Normal" alignment="centred"><EC-RadioButton id="RadioButton5" groupname="Group0" caption="Normal Scale" enabled="true" visible="true" selected="false"></EC-RadioButton><EC-RadioButton id="RadioButton6" groupname="Group0" caption="Log Scale" enabled="true" visible="true" selected="false"></EC-RadioButton><Equation executable="false" style="2D Math" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2I1EhRicvJSxtYXRodmFyaWFudEdRJ25vcm1hbEYn">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=</Equation></Text-field>
</Input>
</Group></Presentation-Block><Presentation-Block>
<Group view="presentation" hide-input="false" hide-output="true" inline-output="false" labelreference="L2268" drawlabel="true">
<Input>
<Text-field style="Text" layout="Normal" alignment="centred"><Equation executable="false" style="2D Math" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2I1EhRicvJSxtYXRodmFyaWFudEdRJ25vcm1hbEYn">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=</Equation></Text-field>
</Input>
</Group></Presentation-Block><Presentation-Block>
<Group view="presentation" hide-input="false" hide-output="true" inline-output="false" labelreference="L2270" drawlabel="true">
<Input>
<Text-field style="Text" layout="Normal" alignment="centred"></Text-field>
</Input>
</Group></Presentation-Block><Presentation-Block>
<Group view="presentation" hide-input="false" hide-output="true" inline-output="false" labelreference="L2144" drawlabel="true">
<Input>
<Text-field style="Text" layout="Normal" alignment="centred"><EC-Button id="Button5" caption="Generate and Plot Binomial Tree" pixel-width="300" pixel-height="200" enabled="true" visible="true" show-border="true" user-size="false"><MapleCode action="click-event-handler">use DocumentTools, Finance, plots in 
#module()

Do(S0= %TextArea26);  
Do(r= %TextArea27); 
Do(sigma= %TextArea28);  
Do(d= %TextArea29); 
Do(t= %TextArea30);  
Do(N= %TextArea32); 
Do(NP=%TextArea31); 

Do(SetEvaluationDate(%TextArea22)):	
Do(Settings(daycounter=h)):

Do(scl=DocumentTools[GetProperty]('RadioButton5','value')):
if scl=&quot;true&quot; then 
	Do(sca=1):
	else
	Do(sca=0):
end if:
		
Do(T= BlackScholesBinomialTree(S0, r,d,sigma,t,N)):
Do(TP= BlackScholesBinomialTree(S0, r,d,sigma,t,NP)):

if sca=1 then 
Do(%Plot4=TreePlot(TP, gridlines=true, axes=boxed)):
else
Do(%Plot4=TreePlot(TP, gridlines=true, axes=boxed, scale=logarithmic)):
end if:

Do(SetProperty(Button6,enabled,&quot;true&quot;)):
#end module;
end use; 
</MapleCode></EC-Button></Text-field>
</Input>
</Group></Presentation-Block></Table-Cell><Table-Cell columnspan="1" backgroundstyle="0" rowspan="1" padding="5" fillcolor="[255,255,255]"><Presentation-Block>
<Group view="presentation" hide-input="false" hide-output="true" inline-output="false" labelreference="L9466" drawlabel="true">
<Input>
<Text-field style="Text" italic="true" layout="Normal" alignment="centred"><Equation executable="false" style="2D Math" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2I1EhRicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0Yn">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=</Equation></Text-field>
</Input>
</Group></Presentation-Block><Presentation-Block>
<Group view="presentation" hide-input="false" hide-output="true" inline-output="false" labelreference="L9468" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input>
<Text-field style="Text" italic="true" layout="Normal" alignment="centred"></Text-field>
</Input>
</Group></Presentation-Block><Presentation-Block>
<Group view="presentation" hide-input="false" hide-output="true" inline-output="false" labelreference="L9470" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input>
<Text-field style="Text" italic="true" layout="Normal" alignment="centred"></Text-field>
</Input>
</Group></Presentation-Block><Presentation-Block>
<Group view="presentation" hide-input="false" hide-output="true" inline-output="false" labelreference="L9472" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input>
<Text-field style="Text" italic="true" layout="Normal" alignment="centred"></Text-field>
</Input>
</Group></Presentation-Block><Presentation-Block>
<Group view="presentation" hide-input="false" hide-output="true" inline-output="false" labelreference="L2096" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input>
<Text-field style="Text" italic="true" layout="Normal" alignment="centred"><Font italic="true">Black Scholes Binomial Tree</Font></Text-field>
</Input>
</Group></Presentation-Block><Presentation-Block>
<Group view="presentation" hide-input="false" hide-output="true" inline-output="false" labelreference="L2131" drawlabel="true">
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<Text-field style="Text" layout="Normal" alignment="centred"><Equation executable="false" style="2D Math" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2I1EhRicvJSxtYXRodmFyaWFudEdRJ25vcm1hbEYn">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=</Equation><EC-Button id="Button6" caption="Calculate the Value of the Option" pixel-width="300" pixel-height="200" enabled="true" visible="true" show-border="true" user-size="false"><MapleCode action="click-event-handler">use DocumentTools, Finance, plots in 

Do(a=DocumentTools[GetProperty]('RadioButton1','value')):
Do(b=DocumentTools[GetProperty]('RadioButton2','value')):
Do(c=DocumentTools[GetProperty]('RadioButton3','value')):
Do(d=DocumentTools[GetProperty]('RadioButton4','value')):

if a=&quot;true&quot; then
	Do(f=1);
	elif b=&quot;true&quot; then 
	Do(f=2);
	elif c=&quot;true&quot; then
	Do(f=3);
	elif d=&quot;true&quot; then 
	Do(f=4);
end if;
		
if f=1 then
	Do(Settings(daycounter=Bond)):
	elif f=2 then 
	Do(Settings(daycounter = Thirty360European)):
	elif f=3 then
	Do(Settings(daycounter=ISDA)):
	elif f=4 then 
	Do(Settings(daycounter=Actual360)):
end if;



#Do(Settings(daycounter = Thirty360European)):
Do(A1= BermudanOption(P1, %MathContainer8)):
Do(%MathContainer10=LatticePrice(A1, T, r)):
end use; 
</MapleCode></EC-Button></Text-field>
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</Section><Presentation-Block>
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<Section collapsed="true" MultipleChoiceAnswerIndex="-1" MultipleChoiceRandomizeChoices="false" TrueFalseAnswerIndex="-1" EssayAnswerRows="5" EssayAnswerColumns="60"><Title>
<Text-field style="Heading 1" layout="Heading 1">3. Asian Options</Text-field></Title>
<Section collapsed="true" MultipleChoiceAnswerIndex="-1" MultipleChoiceRandomizeChoices="false" TrueFalseAnswerIndex="-1" EssayAnswerRows="5" EssayAnswerColumns="60"><Title>
<Text-field style="Heading 2" layout="Heading 2">3.1 Definitions</Text-field></Title><Presentation-Block>
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<Input>
<Text-field style="Text" layout="Normal"></Text-field>
</Input>
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<Input>
<Text-field style="Text" layout="Normal">This example demonstrates the use of Maple for computing the price of an Asian option, a derivative security that has gained popularity in financial markets in recent years.  </Text-field>
</Input>
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<Text-field style="Text" layout="Normal">The payoff of an Asian option is based on the difference between an asset's average price over a given time period, and a fixed price called the strike price. Asian options are popular because they tend to have lower volatility than options whose payoffs are based purely on a single price point.  It is also harder for big traders to manipulate an average price over an extended period than a single price, so Asian options offer further protection against risk.</Text-field>
</Input>
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<Text-field style="Text" layout="Normal"></Text-field>
</Input>
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<Text-field style="Text" layout="Normal">One disadvantage of Asian options is that their prices are very hard to compute using standard techniques.  Unlike European options, which can be priced using the classic Black-Scholes formula, there is no analytical formula for pricing an Asian option when the underlying asset is assumed to have a lognormal distribution, which is par for the course in financial modeling.</Text-field>
<Text-field style="Text" layout="Normal"></Text-field>
<Text-field style="Text" layout="Normal">In this application, we use two different approaches for computing these prices numerically: (1) Solving a partial differential equation, and (2) Monte Carlo simulation.  We will see that the two numerical solutions that Maple derives are the same, providing strong validation for both the techniques and Maple's numerics.</Text-field>
</Input>
<Input>
<Text-field style="Text" layout="Normal"></Text-field>
<Text-field style="Text" layout="Normal">Arithmetic average Asian options are securities whose payoff depends on the average of the underlying stock price over a certain period of time. To be more precise, the value of the continuous arithmetic Asian call option at time<Font style="2D Math"> </Font><Equation executable="false" style="2D Math" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2I1EhRictRiM2Ji1GLDYmUSJ0RicvJSdpdGFsaWNHUSV0cnVlRicvJStiYWNrZ3JvdW5kR1EoWzAsMCwwXUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JI21vR0YkNi5RJSZsZTtGJ0Y3L0Y7USdub3JtYWxGJy8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGRS8lKXN0cmV0Y2h5R0ZFLyUqc3ltbWV0cmljR0ZFLyUobGFyZ2VvcEdGRS8lLm1vdmFibGVsaW1pdHNHRkUvJSdhY2NlbnRHRkUvJSdsc3BhY2VHUSYwLjBlbUYnLyUncnNwYWNlR0ZULUYsNiZRIlRGJ0Y0RjdGOkZBRitGQQ==">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2I1EhRictRiM2Ji1GLDYmUSJ0RicvJSdpdGFsaWNHUSV0cnVlRicvJStiYWNrZ3JvdW5kR1EoWzAsMCwwXUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JI21vR0YkNi5RJSZsZTtGJ0Y3L0Y7USdub3JtYWxGJy8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGRS8lKXN0cmV0Y2h5R0ZFLyUqc3ltbWV0cmljR0ZFLyUobGFyZ2VvcEdGRS8lLm1vdmFibGVsaW1pdHNHRkUvJSdhY2NlbnRHRkUvJSdsc3BhY2VHUSYwLjBlbUYnLyUncnNwYWNlR0ZULUYsNiZRIlRGJ0Y0RjdGOkZBRitGQQ==</Equation> is given by</Text-field>
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<Text-field style="Text" layout="Normal"></Text-field>
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<Text-field style="Text" layout="Normal"><Equation executable="false" style="2D Math" input-equation="" display="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">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</Equation> </Text-field>
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<Text-field style="Text" layout="Normal">where <Equation executable="false" style="2D Math" input-equation="" display="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">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</Equation> is the stock price at time <Equation executable="false" style="2D Math" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JlEidEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUrYmFja2dyb3VuZEdRKFswLDAsMF1GJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRicvRjZRJ25vcm1hbEYn">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JlEidEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUrYmFja2dyb3VuZEdRKFswLDAsMF1GJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRicvRjZRJ25vcm1hbEYn</Equation>, <Equation executable="false" style="2D Math" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JlEiVEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUrYmFja2dyb3VuZEdRKFswLDAsMF1GJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRicvRjZRJ25vcm1hbEYn">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JlEiVEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUrYmFja2dyb3VuZEdRKFswLDAsMF1GJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRicvRjZRJ25vcm1hbEYn</Equation> is the expiration date, and <Equation executable="false" style="2D Math" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JlEiS0YnLyUnaXRhbGljR1EldHJ1ZUYnLyUrYmFja2dyb3VuZEdRKFswLDAsMF1GJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRicvRjZRJ25vcm1hbEYn">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JlEiS0YnLyUnaXRhbGljR1EldHJ1ZUYnLyUrYmFja2dyb3VuZEdRKFswLDAsMF1GJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRicvRjZRJ25vcm1hbEYn</Equation> is the strike price. </Text-field>
<Text-field style="Text" layout="Normal"></Text-field>
<Text-field style="Text" layout="Normal">Since no general closed form solution for the price of the arithmetic average Asian option is known, a variety of numerical methods have been developed. These include formulation as a PDE, Monte Carlo simulation, and numeric inversion of the Laplace transform. </Text-field>
<Text-field style="Text" layout="Normal"></Text-field>
<Text-field style="Text" layout="Normal">This worksheet demonstrates how these methods can be easily and quickly implemented in Maple.</Text-field>
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</Section>
<Section collapsed="true" MultipleChoiceAnswerIndex="-1" MultipleChoiceRandomizeChoices="false" TrueFalseAnswerIndex="-1" EssayAnswerRows="5" EssayAnswerColumns="60"><Title>
<Text-field style="Heading 2" layout="Heading 2">3.2 Numerical Solution of  Vercer's PDE</Text-field></Title>
<Section collapsed="true" MultipleChoiceAnswerIndex="-1" MultipleChoiceRandomizeChoices="false" TrueFalseAnswerIndex="-1" EssayAnswerRows="5" EssayAnswerColumns="60"><Title>
<Text-field style="Heading 3" layout="Heading 3">3.2.1 Mathematical Framework</Text-field></Title><Presentation-Block>
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<Text-field style="Text" layout="Normal"><Equation executable="false" style="2D Math" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2I1EhRicvJSxtYXRodmFyaWFudEdRJ25vcm1hbEYn">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=</Equation></Text-field>
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<Text-field style="Text" layout="Normal">It was shown by Vecer (&quot;A new PDE approach for pricing arithmetic average Asian options&quot;, Journal of Computational Finance, vol. 4, No. 4, 105-113) that the value of the Asian option at time <Equation executable="false" style="2D Math" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbW5HRiQ2JVEiMEYnLyUrYmFja2dyb3VuZEdRKFswLDAsMF1GJy8lLG1hdGh2YXJpYW50R1Enbm9ybWFsRidGMg==">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbW5HRiQ2JVEiMEYnLyUrYmFja2dyb3VuZEdRKFswLDAsMF1GJy8lLG1hdGh2YXJpYW50R1Enbm9ybWFsRidGMg==</Equation> is given by</Text-field>
<Text-field style="Text" layout="Normal"></Text-field>
<Text-field style="Text" alignment="centred" firstindent="0" spacebelow="0" leftmargin="0" linespacing="0.0" initial="0" linebreak="space" rightmargin="0" bulletsuffix="" spaceabove="0" bullet="none" pagebreak-before="false"><Equation executable="false" style="2D Math" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2I1EhRictRiM2KkYrLUklbXN1YkdGJDYlLUYsNiZRIlNGJy8lJ2l0YWxpY0dRJXRydWVGJy8lK2JhY2tncm91bmRHUShbMCwwLDBdRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUYjNiQtSSNtbkdGJDYlUSIwRidGOi9GPlEnbm9ybWFsRidGRi8lL3N1YnNjcmlwdHNoaWZ0R0ZFLUkjbW9HRiQ2LVExJkludmlzaWJsZVRpbWVzO0YnRkYvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRlAvJSlzdHJldGNoeUdGUC8lKnN5bW1ldHJpY0dGUC8lKGxhcmdlb3BHRlAvJS5tb3ZhYmxlbGltaXRzR0ZQLyUnYWNjZW50R0ZQLyUnbHNwYWNlR1EmMC4wZW1GJy8lJ3JzcGFjZUdGaW4tRiw2JlEidUYnRjdGOkY9RkotRiM2Ji1GSzYuUSIoRidGOkZGL0ZPRjlGUS9GVEY5RlVGV0ZZRmVuL0ZoblEsMC4xNjY2NjY3ZW1GJy9GW29GZ28tRiM2J0ZCLUZLNi5RIixGJ0Y6RkZGTi9GUkY5RlNGVUZXRllGZW5GZ24vRltvUSwwLjMzMzMzMzNlbUYnLUkmbWZyYWNHRiQ2KS1GIzYnRistRiM2J0YrRjEtRks2LlEoJm1pbnVzO0YnRjpGRkZORlFGU0ZVRldGWUZlbi9GaG5RLDAuMjIyMjIyMmVtRicvRltvRlxxLUYsNiZRIktGJ0Y3RjpGPUZGRitGOkZGLUYjNidGK0YxRitGOkZGLyUubGluZXRoaWNrbmVzc0dRIjFGJy8lK2Rlbm9tYWxpZ25HUSdjZW50ZXJGJy8lKW51bWFsaWduR0ZocS8lKWJldmVsbGVkR0ZQRjpGK0ZGLUZLNi5RIilGJ0Y6RkZGZG9GUUZlb0ZVRldGWUZlbkZmby9GW29RLDAuMTExMTExMWVtRidGRkYrRkZGK0ZG">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2I1EhRictRiM2KkYrLUklbXN1YkdGJDYlLUYsNiZRIlNGJy8lJ2l0YWxpY0dRJXRydWVGJy8lK2JhY2tncm91bmRHUShbMCwwLDBdRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUYjNiQtSSNtbkdGJDYlUSIwRidGOi9GPlEnbm9ybWFsRidGRi8lL3N1YnNjcmlwdHNoaWZ0R0ZFLUkjbW9HRiQ2LVExJkludmlzaWJsZVRpbWVzO0YnRkYvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRlAvJSlzdHJldGNoeUdGUC8lKnN5bW1ldHJpY0dGUC8lKGxhcmdlb3BHRlAvJS5tb3ZhYmxlbGltaXRzR0ZQLyUnYWNjZW50R0ZQLyUnbHNwYWNlR1EmMC4wZW1GJy8lJ3JzcGFjZUdGaW4tRiw2JlEidUYnRjdGOkY9RkotRiM2Ji1GSzYuUSIoRidGOkZGL0ZPRjlGUS9GVEY5RlVGV0ZZRmVuL0ZoblEsMC4xNjY2NjY3ZW1GJy9GW29GZ28tRiM2J0ZCLUZLNi5RIixGJ0Y6RkZGTi9GUkY5RlNGVUZXRllGZW5GZ24vRltvUSwwLjMzMzMzMzNlbUYnLUkmbWZyYWNHRiQ2KS1GIzYnRistRiM2J0YrRjEtRks2LlEoJm1pbnVzO0YnRjpGRkZORlFGU0ZVRldGWUZlbi9GaG5RLDAuMjIyMjIyMmVtRicvRltvRlxxLUYsNiZRIktGJ0Y3RjpGPUZGRitGOkZGLUYjNidGK0YxRitGOkZGLyUubGluZXRoaWNrbmVzc0dRIjFGJy8lK2Rlbm9tYWxpZ25HUSdjZW50ZXJGJy8lKW51bWFsaWduR0ZocS8lKWJldmVsbGVkR0ZQRjpGK0ZGLUZLNi5RIilGJ0Y6RkZGZG9GUUZlb0ZVRldGWUZlbkZmby9GW29RLDAuMTExMTExMWVtRidGRkYrRkZGK0ZG</Equation> </Text-field>
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<Text-field style="Text" alignment="left" firstindent="0" spacebelow="0" leftmargin="0" linespacing="0.0" initial="0" linebreak="space" rightmargin="0" bulletsuffix="" spaceabove="0" bullet="none" pagebreak-before="false">where the function <Equation executable="false" style="2D Math" input-equation="" display="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">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</Equation> satisfies the following PDE</Text-field>
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<Text-field style="Heading 3" layout="Heading 3">3.2.2  Numerical solution to  Vecer's PDE</Text-field></Title><Presentation-Block>
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<Text-field style="Text" layout="Normal"><Equation executable="false" style="2D Math" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2I1EhRicvJSxtYXRodmFyaWFudEdRJ25vcm1hbEYn">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=</Equation></Text-field>
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<Text-field style="Text" layout="Normal"><Font bold="true" italic="true">Step 1. Set the Partial Differential Equation</Font></Text-field>
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<Text-field style="Text" layout="Normal"><Font bold="true" italic="true">Step 2. Set the Boundary conditions</Font></Text-field>
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<Text-field style="Text" layout="Normal"><Font bold="true" italic="true">Step 3. Define the numerical parameters.</Font></Text-field>
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<Text-field style="Text" layout="Normal"><Font bold="true" italic="true">Step 4. Produce solution &quot;procedure&quot;</Font>

Notice that the solution produces a Maple Module. This module is then invoked to generate the actual paths.</Text-field>
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<Text-field prompt="&gt; " style="Maple Input" layout="Normal"><Equation executable="true" style="2D Input" input-equation="" display="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">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</Equation></Text-field>
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<Group view="presentation" hide-input="true" hide-output="false" inline-output="false" labelreference="L1319" drawlabel="true" redirect-source="L1302">
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<Text-field prompt="&gt; " style="Maple Input" layout="Normal">print(<Label label="L1302" view="label" executable="true"></Label>); # input placeholder</Text-field>
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<Group view="presentation" hide-input="false" hide-output="true" inline-output="false" labelreference="L1320" drawlabel="true" redirect-target="L1322">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal"><Equation executable="true" style="2D Input" input-equation="" display="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">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYxLUkjbWlHRiQ2JVEkdmFsRicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUkjbW9HRiQ2LVEjOj1GJy9GM1Enbm9ybWFsRicvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRj0vJSlzdHJldGNoeUdGPS8lKnN5bW1ldHJpY0dGPS8lKGxhcmdlb3BHRj0vJS5tb3ZhYmxlbGltaXRzR0Y9LyUnYWNjZW50R0Y9LyUnbHNwYWNlR1EsMC4yNzc3Nzc4ZW1GJy8lJ3JzcGFjZUdGTC1GLDYlUSRwZHNGJ0YvRjItRjY2LVEjOi1GJ0Y5RjtGPkZARkJGREZGRkgvRktRJjAuMGVtRicvRk5GVi1GLDYlUSZ2YWx1ZUYnRi9GMi1JKG1mZW5jZWRHRiQ2JC1GIzYoLUYsNiNRIUYnLUYjNiYtRiw2JVEidEYnRi9GMi1GNjYtUSI9RidGOUY7Rj5GQEZCRkRGRkZIRkpGTS1JI21uR0YkNiRRIjBGJ0Y5RjktRjY2LVEiLEYnRjlGOy9GP0YxRkBGQkZERkZGSEZVL0ZOUSwwLjMzMzMzMzNlbUYnLUYjNiYtRiw2JVEnb3V0cHV0RidGL0YyRmJvLUYsNiVRLmxpc3Rwcm9jZWR1cmVGJ0YvRjJGOUZqbkY5RjktRjY2LVEiOkYnRjlGO0Y+RkBGQkZERkZGSEZKRk0tSSdtc3BhY2VHRiQ2Ji8lJ2hlaWdodEdRJjAuMGV4RicvJSZ3aWR0aEdGVi8lJmRlcHRoR0ZfcS8lKmxpbmVicmVha0dRKG5ld2xpbmVGJy1GLDYlUSJ2RidGL0YyRjUtRiw2JVElZXZhbEYnRi9GMi1GZm42JC1GIzYnRmpuLUYjNiYtRiw2JVEidUYnRi9GMi1GNjYtUTAmQXBwbHlGdW5jdGlvbjtGJ0Y5RjtGPkZARkJGREZGRkhGVUZXLUZmbjYkLUYjNiZGX29GaW8tRiw2JVEiekYnRi9GMkY5RjlGOUZpb0YrRjlGOS1GNjYtUSI7RidGOUY7RlxwRkBGQkZERkZGSEZVRk0vJStleGVjdXRhYmxlR0Y9Rjk=</Equation></Text-field>
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<Text-field superscript="false" placeholder="false" executable="false" selection-placeholder="false" italic="false" size="12" bold="false" subscript="false" family="Times New Roman" opaque="false" underline="false" background="[255,255,255]" readonly="false" foreground="[0,0,0]" alignment="centred" firstindent="0" spacebelow="0" leftmargin="0" linespacing="0.0" initial="0" linebreak="space" rightmargin="0" bulletsuffix="" spaceabove="0" bullet="none" pagebreak-before="false"><Equation executable="false" style="2D Output" display="LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVE1b3V0cHV0fnJlZGlyZWN0ZWQuLi5GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRic=">LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVE1b3V0cHV0fnJlZGlyZWN0ZWQuLi5GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRic=</Equation></Text-field>
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<Group view="presentation" hide-input="true" hide-output="false" inline-output="false" labelreference="L1322" drawlabel="true" redirect-source="L1320">
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<Text-field prompt="&gt; " style="Maple Input" layout="Normal">print(<Label label="L1320" view="label" executable="true"></Label>); # input placeholder</Text-field>
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<Text-field style="Text" layout="Normal"><Font bold="true" italic="true">Step 5. Visualize the solution of the PDE</Font></Text-field>
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<Text-field style="Text" layout="Normal"><Equation executable="false" style="2D Math" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2I1EhRicvJSxtYXRodmFyaWFudEdRJ25vcm1hbEYn">JSFH</Equation><Equation executable="true" style="2D Input" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2I1EhRicvJStleGVjdXRhYmxlR1EmZmFsc2VGJy8lLG1hdGh2YXJpYW50R1Enbm9ybWFsRic=">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=</Equation></Text-field>
</Input>
</Group></Presentation-Block><Presentation-Block><CodeEditor-ExecGroup view="presentation" hide-input="false" hide-output="true" inline-output="false" labelreference="L9456" display="code"><EC-CodeEditor id="CodeEditRegion1" visible="false" pixel-width="500" pixel-height="200" code-language="text/maple" autoexpand="true" wrapping="false" show-border="true" code-line-numbers="true"># RESTART AND LOAD PACKAGES
restart:
with(Finance):
with(plots):</EC-CodeEditor></CodeEditor-ExecGroup></Presentation-Block><Presentation-Block>
<Group view="presentation" hide-input="false" hide-output="true" inline-output="false" labelreference="L9351" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal"><Equation executable="true" style="2D Input" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2I1EhRicvJStleGVjdXRhYmxlR1EmZmFsc2VGJy8lLG1hdGh2YXJpYW50R1Enbm9ybWFsRic=">JSFH</Equation></Text-field>
</Input>
</Group></Presentation-Block><Table interior="all" showinput="true" alignment="left" exterior="all" width="87.92528352234824%" labelreference="L1516" showlabel="true" captionalignment="0" title="" drawtitle="false" order="row" drawcaption="false" randomized="false" captionposition="1" plotalignlists="" pagebreak="cell" postexecute="insert" showgroup="true"><Table-Column weight="338" separator="true"></Table-Column><Table-Column weight="450" separator="true"></Table-Column><Table-Column weight="530" separator="true"></Table-Column><Table-Row align="top" separator="true"><Table-Cell columnspan="1" backgroundstyle="0" rowspan="1" padding="5" fillcolor="[255,255,255]"><Presentation-Block>
<Group view="presentation" hide-input="false" hide-output="true" inline-output="false" labelreference="L1541" drawlabel="true">
<Input>
<Text-field style="Text" italic="true" layout="Normal" alignment="centred"><Font italic="true">Parameters</Font></Text-field>
</Input>
</Group></Presentation-Block><Presentation-Block>
<Group view="presentation" hide-input="false" hide-output="true" inline-output="false" labelreference="L1543" drawlabel="true">
<Input>
<Text-field style="Text" italic="true" layout="Normal" alignment="centred"></Text-field>
</Input>
</Group></Presentation-Block><Presentation-Block>
<Group view="presentation" hide-input="false" hide-output="true" inline-output="false" labelreference="L1520" drawlabel="true">
<Input>
<Text-field style="Text" italic="true" layout="Normal" alignment="centred"><EC-TextArea id="TextArea0" enabled="true" visible="true" visiblecharacterwidth="10" visiblerows="1" contents="1" editable="true" wrapping="true" show-border="true" password="false"></EC-TextArea><Font italic="true">   T</Font></Text-field>
</Input>
</Group></Presentation-Block><Presentation-Block>
<Group view="presentation" hide-input="false" hide-output="true" inline-output="false" labelreference="L1528" drawlabel="true">
<Input>
<Text-field style="Text" italic="true" layout="Normal" alignment="centred"><EC-TextArea id="TextArea1" enabled="true" visible="true" visiblecharacterwidth="10" visiblerows="1" contents="100" editable="true" wrapping="true" show-border="true" password="false"></EC-TextArea><Font italic="true"> S0</Font></Text-field>
</Input>
</Group></Presentation-Block><Presentation-Block>
<Group view="presentation" hide-input="false" hide-output="true" inline-output="false" labelreference="L1530" drawlabel="true">
<Input>
<Text-field style="Text" italic="true" layout="Normal" alignment="centred"><EC-TextArea id="TextArea2" enabled="true" visible="true" visiblecharacterwidth="10" visiblerows="1" contents="100" editable="true" wrapping="true" show-border="true" password="false"></EC-TextArea><Font italic="true">   K</Font></Text-field>
</Input>
</Group></Presentation-Block><Presentation-Block>
<Group view="presentation" hide-input="false" hide-output="true" inline-output="false" labelreference="L1532" drawlabel="true">
<Input>
<Text-field style="Text" italic="true" layout="Normal" alignment="centred"><EC-TextArea id="TextArea3" enabled="true" visible="true" visiblecharacterwidth="10" visiblerows="1" contents="0.2" editable="true" wrapping="true" show-border="true" password="false"></EC-TextArea><Font encoding="UTF-8" italic="true">    \317\203</Font></Text-field>
</Input>
</Group></Presentation-Block><Presentation-Block>
<Group view="presentation" hide-input="false" hide-output="true" inline-output="false" labelreference="L1534" drawlabel="true">
<Input>
<Text-field style="Text" italic="true" layout="Normal" alignment="centred"><EC-TextArea id="TextArea4" enabled="true" visible="true" visiblecharacterwidth="10" visiblerows="1" contents="0.15" editable="true" wrapping="true" show-border="true" password="false"></EC-TextArea><Font italic="true">    r</Font></Text-field>
</Input>
</Group></Presentation-Block></Table-Cell><Table-Cell columnspan="1" backgroundstyle="0" rowspan="1" padding="5" fillcolor="[255,255,255]"><Presentation-Block>
<Group view="presentation" hide-input="false" hide-output="true" inline-output="false" labelreference="L1545" drawlabel="true">
<Input>
<Text-field style="Text" italic="true" layout="Normal" alignment="centred"><Font italic="true">Payoff Function</Font></Text-field>
</Input>
</Group></Presentation-Block><Presentation-Block>
<Group view="presentation" hide-input="false" hide-output="true" inline-output="false" labelreference="L1547" drawlabel="true">
<Input>
<Text-field style="Text" italic="true" layout="Normal" alignment="centred"></Text-field>
</Input>
</Group></Presentation-Block><Presentation-Block>
<Group view="presentation" hide-input="false" hide-output="true" inline-output="false" labelreference="L1521" drawlabel="true">
<Input>
<Text-field style="Text" italic="true" layout="Normal" alignment="centred"><EC-MathContainer id="MathContainer0" pixel-width="300" pixel-height="125" expression="&lt;math xmlns='http://www.w3.org/1998/Math/MathML'&gt;&lt;mstyle fontfamily='Times New Roman' mathsize='12pt' mathcolor='#000000'  veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.7099999785423279' scriptminsize='8.0pt'&gt;&lt;mrow&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi mathvariant='normal' fontweight='normal'&gt;max&lt;/mi&gt;&lt;mfenced open='(' close=')' separators=','&gt;&lt;mrow&gt;&lt;mrow&gt;&lt;mfrac&gt;&lt;mrow&gt;&lt;mn fontweight='normal'&gt;1&lt;/mn&gt;&lt;mo fontweight='normal' lspace='0.0em' rspace='0.0em'&gt;&amp;InvisibleTimes;&lt;/mo&gt;&lt;mrow&gt;&lt;msubsup&gt;&lt;mo mathcolor='#909090' color='#909090' fontweight='normal' lspace='0.0em' rspace='0.0em' stretchy='true' largeop='true'&gt;&amp;int;&lt;/mo&gt;&lt;mn fontweight='normal'&gt;0&lt;/mn&gt;&lt;mi fontweight='normal'&gt;t&lt;/mi&gt;&lt;/msubsup&gt;&lt;mrow&gt;&lt;mi fontweight='normal'&gt;X&lt;/mi&gt;&lt;mo fontweight='normal' lspace='0.0em' rspace='0.0em'&gt;&amp;ApplyFunction;&lt;/mo&gt;&lt;mfenced open='(' close=')' separators=','&gt;&lt;mrow&gt;&lt;mi fontweight='normal'&gt;u&lt;/mi&gt;&lt;/mrow&gt;&lt;/mfenced&gt;&lt;/mrow&gt;&lt;mspace height='0.0ex' width='0.3em' depth='0.0ex' linebreak='auto'/&gt;&lt;mo mathcolor='#909090' color='#909090' fontweight='normal' lspace='0.0em' rspace='0.0em'&gt;&amp;DifferentialD;&lt;/mo&gt;&lt;mi fontweight='normal'&gt;u&lt;/mi&gt;&lt;/mrow&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi fontweight='normal'&gt;t&lt;/mi&gt;&lt;/mrow&gt;&lt;/mfrac&gt;&lt;mo fontweight='normal' lspace='0.2222222em' rspace='0.2222222em'&gt;&amp;minus;&lt;/mo&gt;&lt;mi fontweight='normal'&gt;K&lt;/mi&gt;&lt;/mrow&gt;&lt;mo fontweight='normal' separator='true' lspace='0.0em' rspace='0.3333333em'&gt;&amp;comma;&lt;/mo&gt;&lt;mn fontweight='normal'&gt;0&lt;/mn&gt;&lt;/mrow&gt;&lt;/mfenced&gt;&lt;mspace height='0.0ex' width='1.0em' depth='0.0ex' linebreak='nobreak'/&gt;&lt;/mrow&gt;&lt;/mstyle&gt;&lt;/math&gt;" visible="true" show-border="true" autofit="false"></EC-MathContainer></Text-field>
</Input>
</Group></Presentation-Block><Presentation-Block>
<Group view="presentation" hide-input="false" hide-output="true" inline-output="false" labelreference="L1538" drawlabel="true">
<Input>
<Text-field style="Text" italic="true" layout="Normal" alignment="centred"></Text-field>
</Input>
</Group></Presentation-Block><Presentation-Block>
<Group view="presentation" hide-input="false" hide-output="true" inline-output="false" labelreference="L1539" drawlabel="true">
<Input>
<Text-field style="Text" italic="true" layout="Normal" alignment="centred"></Text-field>
</Input>
</Group></Presentation-Block></Table-Cell><Table-Cell columnspan="1" backgroundstyle="0" rowspan="1" padding="5" fillcolor="[255,255,255]"><Presentation-Block>
<Group view="presentation" hide-input="false" hide-output="true" inline-output="false" labelreference="L1522" drawlabel="true">
<Input>
<Text-field style="Text" italic="true" layout="Normal" alignment="centred"><Font italic="true">Parameters of the simulation</Font></Text-field>
</Input>
</Group></Presentation-Block><Presentation-Block>
<Group view="presentation" hide-input="false" hide-output="true" inline-output="false" labelreference="L1550" drawlabel="true">
<Input>
<Text-field style="Text" italic="true" layout="Normal" alignment="centred"></Text-field>
</Input>
</Group></Presentation-Block><Presentation-Block>
<Group view="presentation" hide-input="false" hide-output="true" inline-output="false" labelreference="L1551" drawlabel="true">
<Input>
<Text-field style="Text" italic="true" layout="Normal" alignment="centred"><Font italic="true">Timesteps</Font></Text-field>
</Input>
</Group></Presentation-Block><Presentation-Block>
<Group view="presentation" hide-input="false" hide-output="true" inline-output="false" labelreference="L1552" drawlabel="true">
<Input>
<Text-field style="Text" italic="true" layout="Normal" alignment="centred"><EC-TextArea id="TextArea5" enabled="true" visible="true" visiblecharacterwidth="10" visiblerows="1" contents="10" editable="true" wrapping="true" show-border="true" password="false"></EC-TextArea></Text-field>
</Input>
</Group></Presentation-Block><Presentation-Block>
<Group view="presentation" hide-input="false" hide-output="true" inline-output="false" labelreference="L1557" drawlabel="true">
<Input>
<Text-field style="Text" italic="true" layout="Normal" alignment="centred"></Text-field>
</Input>
</Group></Presentation-Block><Presentation-Block>
<Group view="presentation" hide-input="false" hide-output="true" inline-output="false" labelreference="L1554" drawlabel="true">
<Input>
<Text-field style="Text" italic="true" layout="Normal" alignment="centred"><Font italic="true">Number of replications</Font></Text-field>
</Input>
</Group></Presentation-Block><Presentation-Block>
<Group view="presentation" hide-input="false" hide-output="true" inline-output="false" labelreference="L1555" drawlabel="true">
<Input>
<Text-field style="Text" italic="true" layout="Normal" alignment="centred"><EC-TextArea id="TextArea6" enabled="true" visible="true" visiblecharacterwidth="10" visiblerows="1" contents="10000" editable="true" wrapping="true" show-border="true" password="false"></EC-TextArea></Text-field>
</Input>
</Group></Presentation-Block><Presentation-Block>
<Group view="presentation" hide-input="false" hide-output="true" inline-output="false" labelreference="L1548" drawlabel="true">
<Input>
<Text-field style="Text" italic="true" layout="Normal" alignment="centred"></Text-field>
</Input>
</Group></Presentation-Block></Table-Cell></Table-Row><Table-Row align="top" separator="true"><Table-Cell columnspan="1" backgroundstyle="0" rowspan="1" padding="5" fillcolor="[255,255,255]"><Presentation-Block>
<Group view="presentation" hide-input="false" hide-output="true" inline-output="false" labelreference="L1603" drawlabel="true">
<Input>
<Text-field style="Text" layout="Normal" alignment="centred"><Equation executable="false" style="2D Math" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2I1EhRicvJSxtYXRodmFyaWFudEdRJ25vcm1hbEYn">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=</Equation></Text-field>
</Input>
</Group></Presentation-Block><Presentation-Block>
<Group view="presentation" hide-input="false" hide-output="true" inline-output="false" labelreference="L1602" drawlabel="true">
<Input>
<Text-field style="Text" layout="Normal" alignment="centred"><EC-Button id="Button0" caption="Calculate the Value of the Asian Option" pixel-width="300" pixel-height="200" enabled="true" visible="true" show-border="true" user-size="false"><MapleCode action="click-event-handler">use DocumentTools, plots, Finance, Statistics in 
#module() 

Do(T = %TextArea0); 
Do(S0= %TextArea1); 
Do(K=%TextArea2):
Do(sigma=%TextArea3):
Do(r=%TextArea4):
Do(ts = %TextArea5); 
Do(rp= %TextArea6); 

Do(X=GeometricBrownianMotion(S0,r,sigma)):
Do(P=unapply(%MathContainer0,t)):
Do(%MathContainer1=DiscountFactor(r, T)*ExpectedValue(P(T), timesteps = ts, replications = rp, output = value)):		

Do(SV=SampleValues(P(T), 'timesteps' = ts, 'replications' = rp)):
Do(SV= Statistics[RemoveInRange](SV, -infinity .. NextAfter(0, infinity))):

Do(%Plot0=Statistics[Histogram](SV, bincount = 20, averageshifted = 4, axes = BOXED, gridlines = true)):
Do(%MathContainer2=DataSummary(SV)):
#Do(A=ExpectedValue(P(T), timesteps = ts, replications = rp, output = value)):
#Do(B=printf(&quot;%20s  =  %a\134n&quot;, op(1,A))): 

#end module;
end use; 
</MapleCode></EC-Button></Text-field>
</Input>
</Group></Presentation-Block><Presentation-Block>
<Group view="presentation" hide-input="false" hide-output="true" inline-output="false" labelreference="L1523" drawlabel="true">
<Input>
<Text-field style="Text" layout="Normal"><Equation executable="false" style="2D Math" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2I1EhRicvJSxtYXRodmFyaWFudEdRJ25vcm1hbEYn">JSFH</Equation></Text-field>
</Input>
</Group></Presentation-Block></Table-Cell><Table-Cell columnspan="1" backgroundstyle="0" rowspan="1" padding="5" fillcolor="[255,255,255]"><Presentation-Block>
<Group view="presentation" hide-input="false" hide-output="true" inline-output="false" labelreference="L1622" drawlabel="true">
<Input>
<Text-field style="Text" layout="Normal" alignment="centred"><Font italic="true">Value of the Asian Option</Font></Text-field>
</Input>
</Group></Presentation-Block><Presentation-Block>
<Group view="presentation" hide-input="false" hide-output="true" inline-output="false" labelreference="L1621" drawlabel="true">
<Input>
<Text-field style="Text" layout="Normal" alignment="centred"><EC-MathContainer id="MathContainer1" pixel-width="150" pixel-height="40" expression="&lt;math xmlns='http://www.w3.org/1998/Math/MathML'&gt;&lt;mstyle fontfamily='Times New Roman' mathsize='12pt' mathcolor='#000000'  veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.7099999785423279' scriptminsize='8.0pt'&gt;&lt;mn fontweight='normal'&gt;7.568954263&lt;/mn&gt;&lt;/mstyle&gt;&lt;/math&gt;" visible="true" show-border="true" autofit="false"></EC-MathContainer></Text-field>
</Input>
</Group></Presentation-Block><Presentation-Block>
<Group view="presentation" hide-input="false" hide-output="true" inline-output="false" labelreference="L1572" drawlabel="true">
<Input>
<Text-field style="Text" layout="Normal" alignment="centred"><Equation executable="false" style="2D Math" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2I1EhRicvJSxtYXRodmFyaWFudEdRJ25vcm1hbEYn">JSFH</Equation></Text-field>
</Input>
</Group></Presentation-Block></Table-Cell><Table-Cell columnspan="1" backgroundstyle="0" rowspan="1" padding="5" fillcolor="[255,255,255]"><Presentation-Block>
<Group view="presentation" hide-input="false" hide-output="true" inline-output="false" labelreference="L1570" drawlabel="true">
<Input>
<Text-field style="Text" layout="Normal" alignment="centred"></Text-field>
</Input>
</Group></Presentation-Block><Presentation-Block>
<Group view="presentation" hide-input="false" hide-output="true" inline-output="false" labelreference="L1525" drawlabel="true">
<Input>
<Text-field style="Text" layout="Normal" alignment="centred"></Text-field>
</Input>
</Group></Presentation-Block></Table-Cell></Table-Row><Table-Row align="top" separator="true"><Table-Cell columnspan="1" backgroundstyle="0" rowspan="1" padding="5" fillcolor="[255,255,255]"><Presentation-Block>
<Group view="presentation" hide-input="false" hide-output="true" inline-output="false" labelreference="L1609" drawlabel="true">
<Input>
<Text-field style="Text" layout="Normal" alignment="centred"></Text-field>
</Input>
</Group></Presentation-Block><Presentation-Block>
<Group view="presentation" hide-input="false" hide-output="true" inline-output="false" labelreference="L1610" drawlabel="true">
<Input>
<Text-field style="Text" layout="Normal" alignment="centred"></Text-field>
</Input>
</Group></Presentation-Block><Presentation-Block>
<Group view="presentation" hide-input="false" hide-output="true" inline-output="false" labelreference="L1562" drawlabel="true">
<Input>
<Text-field style="Text" layout="Normal"><Equation executable="false" style="2D Math" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2I1EhRicvJSxtYXRodmFyaWFudEdRJ25vcm1hbEYn">JSFH</Equation></Text-field>
</Input>
</Group></Presentation-Block></Table-Cell><Table-Cell columnspan="1" backgroundstyle="0" rowspan="1" padding="5" fillcolor="[255,255,255]"><Presentation-Block>
<Group view="presentation" hide-input="false" hide-output="true" inline-output="false" labelreference="L1586" drawlabel="true">
<Input>
<Text-field style="Text" italic="true" layout="Normal"><Equation executable="false" style="2D Math" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2I1EhRicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0Yn">JSFH</Equation></Text-field>
</Input>
</Group>
<Group view="presentation" hide-input="false" hide-output="true" inline-output="false" labelreference="L1563" drawlabel="true">
<Input>
<Text-field style="Text" italic="true" layout="Normal"></Text-field>
</Input>
</Group></Presentation-Block><Presentation-Block>
<Group view="presentation" hide-input="false" hide-output="true" inline-output="false" labelreference="L1618" drawlabel="true">
<Input>
<Text-field style="Text" italic="true" layout="Normal" alignment="centred"><Font italic="true">Pay Off of the Asian Option</Font></Text-field>
</Input>
</Group></Presentation-Block><Presentation-Block>
<Group view="presentation" hide-input="false" hide-output="true" inline-output="false" labelreference="L1619" drawlabel="true">
<Input>
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<Text-field style="Heading 2" layout="Heading 2">3.4 Complex Asian Options with &quot;Regime Changes&quot; in the Stochastic Process of the Underlying Asset</Text-field></Title><Presentation-Block>
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restart:
with(Finance):
with(plots):</EC-CodeEditor></CodeEditor-ExecGroup>
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<Text-field style="Text" layout="Normal" alignment="centred"><Font italic="true">Regime Change Transition Probability Matrix</Font></Text-field>
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<Text-field style="Text" layout="Normal" alignment="centred"><Font italic="true">Number of regime changes per period
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<Text-field style="Text" italic="true" layout="Normal" alignment="centred"><Font italic="true">valuation purposes and plotting purposes</Font></Text-field>
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<Text-field style="Text" italic="true" layout="Normal" alignment="centred"><Font italic="true">Timesteps</Font></Text-field>
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</Input>
</Group></Presentation-Block><Presentation-Block>
<Group view="presentation" hide-input="false" hide-output="true" inline-output="false" labelreference="L1783" drawlabel="true">
<Input>
<Text-field style="Text" layout="Normal" alignment="centred"></Text-field>
</Input>
</Group></Presentation-Block><Presentation-Block>
<Group view="presentation" hide-input="false" hide-output="true" inline-output="false" labelreference="L1927" drawlabel="true">
<Input>
<Text-field style="Text" layout="Normal" alignment="centred"><EC-Button id="Button2" caption="Plot the Stochastic Process" pixel-width="300" pixel-height="200" enabled="true" visible="true" show-border="true" user-size="false"><MapleCode action="click-event-handler">use DocumentTools, plots, Finance, Statistics in 
#module() 

Do(T = %TextArea7); 
Do(S0= %TextArea8); 
Do(K=%TextArea9):
Do(sigma=%TextArea10):
Do(r=%TextArea11):
Do(ts = %TextArea12); 
Do(rp= %TextArea13); 
Do(sigma1=%TextArea17):
Do(r1=%TextArea18):
Do(TPM=%MathContainer6):
Do(sw=%TextArea19):
Do(tsg=%TextArea20):
Do(rpg=%TextArea21):


Do(X1=GeometricBrownianMotion(S0,r,sigma)):
Do(X2=GeometricBrownianMotion(S0, r1, sigma1)):
Do(X= RegimeSwitchingProcess(TPM,&lt;X1, X2&gt;, 1, sw)):

Do(A=SamplePath(X(t), t=0..T, timesteps=tsg, replications=rpg)):
Do(%Plot2=PathPlot(A, gridlines=true)):
#Do(A=ExpectedValue(P(T), timesteps = ts, replications = rp, output = value)):
#Do(B=printf(&quot;%20s  =  %a\134n&quot;, op(1,A))): 

#end module;
end use; </MapleCode></EC-Button></Text-field>
</Input>
</Group></Presentation-Block><Presentation-Block>
<Group view="presentation" hide-input="false" hide-output="true" inline-output="false" labelreference="L1785" drawlabel="true">
<Input>
<Text-field style="Text" layout="Normal" alignment="centred"></Text-field>
</Input>
</Group></Presentation-Block></Table-Cell><Table-Cell columnspan="1" backgroundstyle="0" rowspan="1" padding="5" fillcolor="[255,255,255]"><Presentation-Block>
<Group view="presentation" hide-input="false" hide-output="true" inline-output="false" labelreference="L1763" drawlabel="true">
<Input>
<Text-field style="Text" layout="Normal" alignment="centred"></Text-field>
</Input>
</Group></Presentation-Block><Presentation-Block>
<Group view="presentation" hide-input="false" hide-output="true" inline-output="false" labelreference="L1765" drawlabel="true">
<Input>
<Text-field style="Text" layout="Normal"></Text-field>
</Input>
</Group></Presentation-Block><Presentation-Block>
<Group view="presentation" hide-input="false" hide-output="true" inline-output="false" labelreference="L1817" drawlabel="true">
<Input>
<Text-field style="Text" layout="Normal" alignment="centred"></Text-field>
</Input>
</Group></Presentation-Block></Table-Cell></Table-Row><Table-Row align="top" separator="true"><Table-Cell columnspan="1" backgroundstyle="0" rowspan="1" padding="5" fillcolor="[255,255,255]"><Presentation-Block>
<Group view="presentation" hide-input="false" hide-output="true" inline-output="false" labelreference="L1673" drawlabel="true">
<Input>
<Text-field style="Text" layout="Normal" alignment="centred"></Text-field>
</Input>
</Group></Presentation-Block><Presentation-Block>
<Group view="presentation" hide-input="false" hide-output="true" inline-output="false" labelreference="L1918" drawlabel="true">
<Input>
<Text-field style="Text" italic="true" layout="Normal" alignment="centred"><Font italic="true">Payoff Function</Font></Text-field>
</Input>
</Group></Presentation-Block><Presentation-Block>
<Group view="presentation" hide-input="false" hide-output="true" inline-output="false" labelreference="L1919" drawlabel="true">
<Input>
<Text-field style="Text" italic="true" layout="Normal" alignment="centred"></Text-field>
</Input>
</Group></Presentation-Block><Presentation-Block>
<Group view="presentation" hide-input="false" hide-output="true" inline-output="false" labelreference="L1920" drawlabel="true">
<Input>
<Text-field style="Text" italic="true" layout="Normal" alignment="centred"><EC-MathContainer id="MathContainer3" pixel-width="300" pixel-height="125" expression="&lt;math xmlns='http://www.w3.org/1998/Math/MathML'&gt;&lt;mstyle fontfamily='Times New Roman' mathsize='12pt' mathcolor='#000000'  veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.7099999785423279' scriptminsize='8.0pt'&gt;&lt;mrow&gt;&lt;mi mathvariant='normal' fontweight='normal'&gt;&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi mathvariant='normal' fontweight='normal'&gt;max&lt;/mi&gt;&lt;mfenced open='(' close=')' separators=','&gt;&lt;mrow&gt;&lt;mrow&gt;&lt;mfrac&gt;&lt;mrow&gt;&lt;mn fontweight='normal'&gt;1&lt;/mn&gt;&lt;mo fontweight='normal' lspace='0.0em' rspace='0.0em'&gt;&amp;InvisibleTimes;&lt;/mo&gt;&lt;mrow&gt;&lt;msubsup&gt;&lt;mo mathcolor='#909090' color='#909090' fontweight='normal' lspace='0.0em' rspace='0.0em' stretchy='true' largeop='true'&gt;&amp;int;&lt;/mo&gt;&lt;mn fontweight='normal'&gt;0&lt;/mn&gt;&lt;mi fontweight='normal'&gt;t&lt;/mi&gt;&lt;/msubsup&gt;&lt;mrow&gt;&lt;mi fontweight='normal'&gt;X&lt;/mi&gt;&lt;mo fontweight='normal' lspace='0.0em' rspace='0.0em'&gt;&amp;ApplyFunction;&lt;/mo&gt;&lt;mfenced open='(' close=')' separators=','&gt;&lt;mrow&gt;&lt;mi fontweight='normal'&gt;u&lt;/mi&gt;&lt;/mrow&gt;&lt;/mfenced&gt;&lt;/mrow&gt;&lt;mspace height='0.0ex' width='0.3em' depth='0.0ex' linebreak='auto'/&gt;&lt;mo mathcolor='#909090' color='#909090' fontweight='normal' lspace='0.0em' rspace='0.0em'&gt;&amp;DifferentialD;&lt;/mo&gt;&lt;mi fontweight='normal'&gt;u&lt;/mi&gt;&lt;/mrow&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi fontweight='normal'&gt;t&lt;/mi&gt;&lt;/mrow&gt;&lt;/mfrac&gt;&lt;mo fontweight='normal' lspace='0.2222222em' rspace='0.2222222em'&gt;&amp;minus;&lt;/mo&gt;&lt;mi fontweight='normal'&gt;K&lt;/mi&gt;&lt;/mrow&gt;&lt;mo fontweight='normal' separator='true' lspace='0.0em' rspace='0.3333333em'&gt;&amp;comma;&lt;/mo&gt;&lt;mn fontweight='normal'&gt;0&lt;/mn&gt;&lt;/mrow&gt;&lt;/mfenced&gt;&lt;mspace height='0.0ex' width='1.0em' depth='0.0ex' linebreak='nobreak'/&gt;&lt;/mrow&gt;&lt;/mstyle&gt;&lt;/math&gt;" visible="true" show-border="true" autofit="false"></EC-MathContainer></Text-field>
</Input>
</Group></Presentation-Block><Presentation-Block>
<Group view="presentation" hide-input="false" hide-output="true" inline-output="false" labelreference="L1917" drawlabel="true">
<Input>
<Text-field style="Text" italic="true" layout="Normal" alignment="centred"></Text-field>
</Input>
</Group></Presentation-Block><Presentation-Block>
<Group view="presentation" hide-input="false" hide-output="true" inline-output="false" labelreference="L1853" drawlabel="true">
<Input>
<Text-field style="Text" layout="Normal" alignment="centred"></Text-field>
</Input>
</Group></Presentation-Block><Presentation-Block>
<Group view="presentation" hide-input="false" hide-output="true" inline-output="false" labelreference="L1683" drawlabel="true">
<Input>
<Text-field style="Text" layout="Normal"><Equation executable="false" style="2D Math" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2I1EhRicvJSxtYXRodmFyaWFudEdRJ25vcm1hbEYn">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=</Equation></Text-field>
</Input>
</Group></Presentation-Block></Table-Cell><Table-Cell columnspan="1" backgroundstyle="0" rowspan="1" padding="5" fillcolor="[255,255,255]"><Presentation-Block>
<Group view="presentation" hide-input="false" hide-output="true" inline-output="false" labelreference="L1682" drawlabel="true">
<Input>
<Text-field style="Text" italic="true" layout="Normal"><Equation executable="false" style="2D Math" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2I1EhRicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0Yn">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=</Equation></Text-field>
</Input>
</Group></Presentation-Block><Presentation-Block>
<Group view="presentation" hide-input="false" hide-output="true" inline-output="false" labelreference="L1909" drawlabel="true">
<Input>
<Text-field style="Text" layout="Normal" alignment="centred"></Text-field>
</Input>
</Group></Presentation-Block><Presentation-Block>
<Group view="presentation" hide-input="false" hide-output="true" inline-output="false" labelreference="L1910" drawlabel="true">
<Input>
<Text-field style="Text" layout="Normal" alignment="centred"><Font italic="true">Value of the Asian Option</Font></Text-field>
</Input>
</Group></Presentation-Block><Presentation-Block>
<Group view="presentation" hide-input="false" hide-output="true" inline-output="false" labelreference="L1911" drawlabel="true">
<Input>
<Text-field style="Text" layout="Normal" alignment="centred"><EC-MathContainer id="MathContainer4" pixel-width="100" pixel-height="30" expression="&lt;math xmlns='http://www.w3.org/1998/Math/MathML'&gt;&lt;mstyle fontfamily='Times New Roman' mathsize='12pt' mathcolor='#000000'  veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.7099999785423279' scriptminsize='8.0pt'&gt;&lt;mn fontweight='normal'&gt;10.72623025&lt;/mn&gt;&lt;/mstyle&gt;&lt;/math&gt;" visible="true" show-border="true" autofit="false"></EC-MathContainer></Text-field>
</Input>
</Group></Presentation-Block><Presentation-Block>
<Group view="presentation" hide-input="false" hide-output="true" inline-output="false" labelreference="L1908" drawlabel="true">
<Input>
<Text-field style="Text" layout="Normal" alignment="centred"></Text-field>
</Input>
</Group></Presentation-Block><Presentation-Block>
<Group view="presentation" hide-input="false" hide-output="true" inline-output="false" labelreference="L1912" drawlabel="true">
<Input>
<Text-field style="Text" layout="Normal" alignment="centred"><EC-Button id="Button1" caption="Calculate the Value of the Asian Option" pixel-width="300" pixel-height="200" enabled="true" visible="true" show-border="true" user-size="false"><MapleCode action="click-event-handler">use DocumentTools, plots, Finance, Statistics in 
#module() 

Do(T = %TextArea7); 
Do(S0= %TextArea8); 
Do(K=%TextArea9):
Do(sigma=%TextArea10):
Do(r=%TextArea11):
Do(ts = %TextArea12); 
Do(rp= %TextArea13); 
Do(sigma1=%TextArea17):
Do(r1=%TextArea18):
Do(TPM=%MathContainer6):
Do(sw=%TextArea19):

Do(X1=GeometricBrownianMotion(S0,r,sigma)):
Do(X2=GeometricBrownianMotion(S0, r1, sigma1)):
Do(X= RegimeSwitchingProcess(TPM,&lt;X1, X2&gt;, 1, sw)):

Do(P=unapply(%MathContainer3,t)):
Do(%MathContainer4=DiscountFactor(r, T)*ExpectedValue(P(T), timesteps = ts, replications = rp, output = value)):		

Do(SV=SampleValues(P(T), 'timesteps' = ts, 'replications' = rp)):
Do(SV= Statistics[RemoveInRange](SV, -infinity .. NextAfter(0, infinity))):

Do(%Plot1=Statistics[Histogram](SV, bincount = 20, averageshifted = 4, axes = BOXED, gridlines = true)):
Do(%MathContainer5=DataSummary(SV)):
#Do(A=ExpectedValue(P(T), timesteps = ts, replications = rp, output = value)):
#Do(B=printf(&quot;%20s  =  %a\134n&quot;, op(1,A))): 

#end module;
end use; 
</MapleCode></EC-Button></Text-field>
</Input>
</Group></Presentation-Block><Presentation-Block>
<Group view="presentation" hide-input="false" hide-output="true" inline-output="false" labelreference="L1913" drawlabel="true">
<Input>
<Text-field style="Text" layout="Normal" alignment="centred"></Text-field>
</Input>
</Group></Presentation-Block><Presentation-Block>
<Group view="presentation" hide-input="false" hide-output="true" inline-output="false" labelreference="L1907" drawlabel="true">
<Input>
<Text-field style="Text" italic="true" layout="Normal" alignment="centred"></Text-field>
</Input>
</Group></Presentation-Block><Presentation-Block>
<Group view="presentation" hide-input="false" hide-output="true" inline-output="false" labelreference="L1915" drawlabel="true">
<Input>
<Text-field style="Text" italic="true" layout="Normal" alignment="centred"><Font italic="true">Summary Statistics</Font></Text-field>
</Input>
</Group></Presentation-Block><Presentation-Block>
<Group view="presentation" hide-input="false" hide-output="true" inline-output="false" labelreference="L1914" drawlabel="true">
<Input>
<Text-field style="Text" italic="true" layout="Normal" alignment="centred"><EC-MathContainer id="MathContainer5" pixel-width="300" pixel-height="400" expression="&lt;math xmlns='http://www.w3.org/1998/Math/MathML'&gt;&lt;mstyle fontfamily='Times New Roman' mathsize='12pt' mathcolor='#000000'  veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.7099999785423279' scriptminsize='8.0pt'&gt;&lt;mfenced open='[' close=']' separators=','&gt;&lt;mrow&gt;&lt;mrow&gt;&lt;mi fontweight='normal'&gt;mean&lt;/mi&gt;&lt;mo fontweight='normal' lspace='0.2777778em' rspace='0.2777778em'&gt;&amp;equals;&lt;/mo&gt;&lt;mn fontweight='normal'&gt;21.483811372211726&lt;/mn&gt;&lt;/mrow&gt;&lt;mo fontweight='normal' separator='true' lspace='0.0em' rspace='0.3333333em'&gt;&amp;comma;&lt;/mo&gt;&lt;mrow&gt;&lt;mi fontweight='normal'&gt;standarddeviation&lt;/mi&gt;&lt;mo fontweight='normal' lspace='0.2777778em' rspace='0.2777778em'&gt;&amp;equals;&lt;/mo&gt;&lt;mn fontweight='normal'&gt;18.770512607499562&lt;/mn&gt;&lt;/mrow&gt;&lt;mo fontweight='normal' separator='true' lspace='0.0em' rspace='0.3333333em'&gt;&amp;comma;&lt;/mo&gt;&lt;mrow&gt;&lt;mi fontweight='normal'&gt;skewness&lt;/mi&gt;&lt;mo fontweight='normal' lspace='0.2777778em' rspace='0.2777778em'&gt;&amp;equals;&lt;/mo&gt;&lt;mn fontweight='normal'&gt;1.7170174180018427&lt;/mn&gt;&lt;/mrow&gt;&lt;mo fontweight='normal' separator='true' lspace='0.0em' rspace='0.3333333em'&gt;&amp;comma;&lt;/mo&gt;&lt;mrow&gt;&lt;mi fontweight='normal'&gt;kurtosis&lt;/mi&gt;&lt;mo fontweight='normal' lspace='0.2777778em' rspace='0.2777778em'&gt;&amp;equals;&lt;/mo&gt;&lt;mn fontweight='normal'&gt;8.102904097415198&lt;/mn&gt;&lt;/mrow&gt;&lt;mo fontweight='normal' separator='true' lspace='0.0em' rspace='0.3333333em'&gt;&amp;comma;&lt;/mo&gt;&lt;mrow&gt;&lt;mi fontweight='normal'&gt;minimum&lt;/mi&gt;&lt;mo fontweight='normal' lspace='0.2777778em' rspace='0.2777778em'&gt;&amp;equals;&lt;/mo&gt;&lt;mn fontweight='normal'&gt;0.005695191122100596&lt;/mn&gt;&lt;/mrow&gt;&lt;mo fontweight='normal' separator='true' lspace='0.0em' rspace='0.3333333em'&gt;&amp;comma;&lt;/mo&gt;&lt;mrow&gt;&lt;mi fontweight='normal'&gt;maximum&lt;/mi&gt;&lt;mo fontweight='normal' lspace='0.2777778em' rspace='0.2777778em'&gt;&amp;equals;&lt;/mo&gt;&lt;mn fontweight='normal'&gt;205.31777951221028&lt;/mn&gt;&lt;/mrow&gt;&lt;mo fontweight='normal' separator='true' lspace='0.0em' rspace='0.3333333em'&gt;&amp;comma;&lt;/mo&gt;&lt;mrow&gt;&lt;mi fontweight='normal'&gt;cumulativeweight&lt;/mi&gt;&lt;mo fontweight='normal' lspace='0.2777778em' rspace='0.2777778em'&gt;&amp;equals;&lt;/mo&gt;&lt;mn fontweight='normal'&gt;5607.0&lt;/mn&gt;&lt;/mrow&gt;&lt;/mrow&gt;&lt;/mfenced&gt;&lt;/mstyle&gt;&lt;/math&gt;" visible="true" show-border="true" autofit="false"></EC-MathContainer></Text-field>
</Input>
</Group></Presentation-Block><Presentation-Block>
<Group view="presentation" hide-input="false" hide-output="true" inline-output="false" labelreference="L1906" drawlabel="true">
<Input>
<Text-field style="Text" layout="Normal" alignment="centred"></Text-field>
</Input>
</Group></Presentation-Block><Presentation-Block>
<Group view="presentation" hide-input="false" hide-output="true" inline-output="false" labelreference="L1931" drawlabel="true">
<Input>
<Text-field style="Text" italic="true" layout="Normal"></Text-field>
</Input>
</Group></Presentation-Block></Table-Cell><Table-Cell columnspan="1" backgroundstyle="0" rowspan="1" padding="5" fillcolor="[255,255,255]"><Presentation-Block>
<Group view="presentation" hide-input="false" hide-output="true" inline-output="false" labelreference="L1686" drawlabel="true">
<Input>
<Text-field style="Text" italic="true" layout="Normal" alignment="centred"></Text-field>
</Input>
</Group></Presentation-Block><Presentation-Block>
<Group view="presentation" hide-input="false" hide-output="true" inline-output="false" labelreference="L1864" drawlabel="true">
<Input>
<Text-field style="Text" italic="true" layout="Normal"></Text-field>
</Input>
</Group></Presentation-Block><Presentation-Block>
<Group view="presentation" hide-input="false" hide-output="true" inline-output="false" labelreference="L1865" drawlabel="true">
<Input>
<Text-field style="Text" italic="true" layout="Normal" alignment="centred"><Font italic="true">Pay Off of the Asian Option</Font></Text-field>
</Input>
</Group></Presentation-Block><Presentation-Block>
<Group view="presentation" hide-input="false" hide-output="true" inline-output="false" labelreference="L1866" drawlabel="true">
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<Text-field style="Heading 1" layout="Heading 1">4. European Swaptions</Text-field></Title>
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<Text-field style="Heading 2" layout="Heading 2">4.1. Concept</Text-field></Title>
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<Text-field style="Text" layout="Normal">A swaption is an option granting its owner the right but not the obligation to enter into an underlying swap. Although options can be traded on a variety of swaps, the term &quot;swaption&quot; typically refers to options on interest rate swaps.</Text-field>
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<Text-field style="Text" layout="Normal">There are two types of swaption contracts:</Text-field>
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<Text-field style="Text" layout="Normal">In addition, a &quot;straddle&quot; refers to a combination of a receiver and a payer option on the same underlying swap.</Text-field>
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<Text-field style="Text" layout="Normal">The buyer and seller of the swaption agree on:</Text-field>
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<Text-field style="Text" layout="Normal">The participants in the swaption market are predominantly large corporations, banks, financial institutions and hedge funds. End users such as corporations and banks typically use swaptions to manage interest rate risk arising from their core business or from their financing arrangements. For example, a corporation wanting protection from rising interest rates might buy a payer swaption. A bank that holds a mortgage portfolio might buy a receiver swaption to protect against lower interest rates that might lead to early prepayment of the mortgages. A hedge fund believing that interest rates will not rise by more than a certain amount might sell a payer swaption, aiming to make money by collecting the premium. Major investment and commercial banks such as JP Morgan Chase, Bank of America Securities and Citigroup make markets in swaptions in the major currencies, and these banks trade amongst themselves in the swaption interbank market. The market making banks typically manage large portfolios of swaptions that they have written with various counterparties. A significant investment in technology and human capital is required to properly monitor the resulting exposure. Swaption markets exist in most of the major currencies in the world, the largest markets being in U.S. dollars, euro, sterling and Japanese yen.</Text-field>
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<Text-field style="Text" layout="Normal">The swaption market is over-the-counter (OTC), i.e., not traded on any exchange. Legally, a swaption is a contract granting a party the right to enter an agreement with another counterparty to exchange the required payments. The counterparties are exposed to each other's failure to make scheduled payments on the underlying swap, although this exposure is typically mitigated through the use of collateral agreements whereby variation margin is posted to cover the anticipated future exposure</Text-field>
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<Text-field style="Text" layout="Normal">There are three main categories of Swaption, although exotic desks may be willing to create customised types, analogous to exotic options, in some cases. The standard varieties are</Text-field>
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<Text-field style="Heading 3" layout="Heading 3">4.2.1 Swaptions with Maple</Text-field></Title><Presentation-Block>
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</Group></Presentation-Block><Table interior="group" showinput="true" alignment="left" exterior="all" width="90.56347589952478%" labelreference="L9602" showlabel="true" captionalignment="0" title="" order="row" drawcaption="false" randomized="false" captionposition="1" plotalignlists="" pagebreak="cell" postexecute="insert" showgroup="true"><Table-Column weight="1334" separator="true"></Table-Column><Table-Row align="top" separator="true"><Table-Cell columnspan="1" backgroundstyle="0" rowspan="1" padding="5" fillcolor="[255,255,255]"><Presentation-Block>
<Group view="presentation" hide-input="false" hide-output="true" inline-output="false" labelreference="L9607" drawlabel="true">
<Input>
<Text-field style="Text" layout="Bullet Item">The <Font font_style_name="Help Maple Name" superscript="false" placeholder="false" executable="false" selection-placeholder="false" italic="false" size="12" bold="false" style="Help Maple Name" subscript="false" family="Times New Roman" opaque="false" underline="false" background="[255,255,255]" readonly="false" foreground="[0,0,0]">EuropeanSwaption</Font> command creates a new European-style swaption with the specified payoff and maturity. The swaption can be exercised only at the time or date specified by the <Font font_style_name="Help Maple Name" superscript="false" placeholder="false" executable="false" selection-placeholder="false" italic="false" size="12" bold="false" style="Help Maple Name" subscript="false" family="Times New Roman" opaque="false" underline="false" background="[255,255,255]" readonly="false" foreground="[0,0,0]">exercise</Font> parameter. This is the opposite of an American-style swaption, which can be exercised at any time before the expiration.</Text-field>
<Text-field style="Text" layout="Bullet Item">The parameter <Font font_style_name="Help Maple Name" superscript="false" placeholder="false" executable="false" selection-placeholder="false" italic="false" size="12" bold="false" style="Help Maple Name" subscript="false" family="Times New Roman" opaque="false" underline="false" background="[255,255,255]" readonly="false" foreground="[0,0,0]">swap</Font> is the underlying interest rate swap </Text-field>
<Text-field style="Text" layout="Bullet Item">The parameter exercise specifies the time or date when the option can be exercised. It can be given either as a non-negative constant or as a date in any of the formats recognized by the Finance[ParseDate] command.</Text-field>
<Text-field style="Text" layout="Bullet Item">The LatticePrice command can be used to price a European-style swaption using any given binomial or trinomial tree.</Text-field>
<Text-field style="Text" layout="Normal"></Text-field>
</Input>
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<Group view="presentation" hide-input="false" hide-output="true" inline-output="false" labelreference="L9605" drawlabel="true">
<Input>
<Text-field style="Text" layout="Bullet Item" bullet="none">The sintaxis is as follows:

<Font italic="true">EuropeanSwaption(<Font font_style_name="Help Maple Name" superscript="false" placeholder="false" executable="false" selection-placeholder="false" size="12" bold="false" style="Help Maple Name" subscript="false" family="Times New Roman" opaque="false" background="[255,255,255]" underline="false" readonly="false" foreground="[0,0,0]">irswap</Font>, <Font font_style_name="Help Maple Name" superscript="false" placeholder="false" executable="false" selection-placeholder="false" size="12" bold="false" style="Help Maple Name" subscript="false" family="Times New Roman" opaque="false" background="[255,255,255]" underline="false" readonly="false" foreground="[0,0,0]">exercise</Font>, <Font font_style_name="Help Maple Name" superscript="false" placeholder="false" executable="false" selection-placeholder="false" size="12" bold="false" style="Help Maple Name" subscript="false" family="Times New Roman" opaque="false" background="[255,255,255]" underline="false" readonly="false" foreground="[0,0,0]">opts</Font>)</Font></Text-field>
</Input>
</Group></Presentation-Block><Table interior="group" showinput="true" alignment="left" exterior="none" width="100%" labelreference="L9606" showlabel="true" captionalignment="0" order="row" drawcaption="false" randomized="false" captionposition="1" plotalignlists="" pagebreak="cell" postexecute="insert" showgroup="true"><Table-Column weight="93" separator="false"></Table-Column><Table-Column weight="25" separator="false"></Table-Column><Table-Column weight="632" separator="false"></Table-Column><Table-Row align="baseline" separator="false"><Table-Cell columnspan="1" backgroundstyle="0" rowspan="1" padding="5" fillcolor="[255,255,255]">
<Text-field style="Text" layout="Normal"><Font font_style_name="Help Fixed" superscript="false" placeholder="false" executable="false" selection-placeholder="false" italic="false" size="12" bold="false" style="Help Fixed" subscript="false" family="Times New Roman" opaque="false" underline="false" background="[255,255,255]" readonly="false" foreground="[0,0,0]">swap</Font></Text-field></Table-Cell><Table-Cell columnspan="1" backgroundstyle="0" rowspan="1" padding="5" fillcolor="[255,255,255]">
<Text-field style="Text" layout="Normal"><Font font_style_name="Help Fixed" superscript="false" placeholder="false" executable="false" selection-placeholder="false" italic="false" size="12" bold="false" style="Help Fixed" subscript="false" family="Times New Roman" opaque="false" underline="false" background="[255,255,255]" readonly="false" foreground="[0,0,0]">-</Font></Text-field></Table-Cell><Table-Cell columnspan="1" backgroundstyle="0" rowspan="1" padding="5" fillcolor="[255,255,255]">
<Text-field style="Text" layout="Normal">simple swap data structures; interest rate swap</Text-field></Table-Cell></Table-Row><Table-Row align="baseline" separator="false"><Table-Cell columnspan="1" backgroundstyle="0" rowspan="1" padding="5" fillcolor="[255,255,255]">
<Text-field style="Text" layout="Normal"><Font font_style_name="Help Fixed" superscript="false" placeholder="false" executable="false" selection-placeholder="false" italic="false" size="12" bold="false" style="Help Fixed" subscript="false" family="Times New Roman" opaque="false" underline="false" background="[255,255,255]" readonly="false" foreground="[0,0,0]">exercise</Font></Text-field></Table-Cell><Table-Cell columnspan="1" backgroundstyle="0" rowspan="1" padding="5" fillcolor="[255,255,255]">
<Text-field style="Text" layout="Normal"><Font font_style_name="Help Fixed" superscript="false" placeholder="false" executable="false" selection-placeholder="false" italic="false" size="12" bold="false" style="Help Fixed" subscript="false" family="Times New Roman" opaque="false" underline="false" background="[255,255,255]" readonly="false" foreground="[0,0,0]">-</Font></Text-field></Table-Cell><Table-Cell columnspan="1" backgroundstyle="0" rowspan="1" padding="5" fillcolor="[255,255,255]">
<Text-field style="Text" layout="Normal">a non-negative constant, a string containing a date specification in a format recognized by Finance[ParseDate], or a date data structure; the maturity time or date</Text-field></Table-Cell></Table-Row><Table-Row align="baseline" separator="false"><Table-Cell columnspan="1" backgroundstyle="0" rowspan="1" padding="5" fillcolor="[255,255,255]">
<Text-field style="Text" layout="Normal"><Font font_style_name="Help Fixed" superscript="false" placeholder="false" executable="false" selection-placeholder="false" italic="false" size="12" bold="false" style="Help Fixed" subscript="false" family="Times New Roman" opaque="false" underline="false" background="[255,255,255]" readonly="false" foreground="[0,0,0]">opts</Font></Text-field></Table-Cell><Table-Cell columnspan="1" backgroundstyle="0" rowspan="1" padding="5" fillcolor="[255,255,255]">
<Text-field style="Text" layout="Normal"><Font font_style_name="Help Fixed" superscript="false" placeholder="false" executable="false" selection-placeholder="false" italic="false" size="12" bold="false" style="Help Fixed" subscript="false" family="Times New Roman" opaque="false" underline="false" background="[255,255,255]" readonly="false" foreground="[0,0,0]">-</Font></Text-field></Table-Cell><Table-Cell columnspan="1" backgroundstyle="0" rowspan="1" padding="5" fillcolor="[255,255,255]">
<Text-field style="Text" layout="Normal">(optional) equation(s) of the form <Font font_style_name="Help Maple Name" superscript="false" placeholder="false" executable="false" selection-placeholder="false" italic="false" size="12" bold="false" style="Help Maple Name" subscript="false" family="Times New Roman" opaque="false" underline="false" background="[255,255,255]" readonly="false" foreground="[0,0,0]">option</Font> = <Font font_style_name="Help Maple Name" superscript="false" placeholder="false" executable="false" selection-placeholder="false" italic="false" size="12" bold="false" style="Help Maple Name" subscript="false" family="Times New Roman" opaque="false" underline="false" background="[255,255,255]" readonly="false" foreground="[0,0,0]">value</Font> where <Font font_style_name="Help Maple Name" superscript="false" placeholder="false" executable="false" selection-placeholder="false" italic="false" size="12" bold="false" style="Help Maple Name" subscript="false" family="Times New Roman" opaque="false" underline="false" background="[255,255,255]" readonly="false" foreground="[0,0,0]">option</Font> is one of <Font font_style_name="Help Maple Name" superscript="false" placeholder="false" executable="false" selection-placeholder="false" italic="false" size="12" bold="false" style="Help Maple Name" subscript="false" family="Times New Roman" opaque="false" underline="false" background="[255,255,255]" readonly="false" foreground="[0,0,0]">referencedate</Font> or <Font font_style_name="Help Maple Name" superscript="false" placeholder="false" executable="false" selection-placeholder="false" italic="false" size="12" bold="false" style="Help Maple Name" subscript="false" family="Times New Roman" opaque="false" underline="false" background="[255,255,255]" readonly="false" foreground="[0,0,0]">daycounter</Font>; specify options for the <Font font_style_name="Help Maple Name" superscript="false" placeholder="false" executable="false" selection-placeholder="false" italic="false" size="12" bold="false" style="Help Maple Name" subscript="false" family="Times New Roman" opaque="false" underline="false" background="[255,255,255]" readonly="false" foreground="[0,0,0]">EuropeanSwaption</Font> command</Text-field></Table-Cell></Table-Row></Table><Presentation-Block>
<Group view="presentation" hide-input="false" hide-output="true" inline-output="false" labelreference="L9603" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input>
<Text-field style="Text" layout="Normal"></Text-field>
</Input>
</Group></Presentation-Block></Table-Cell></Table-Row></Table><Presentation-Block>
<Group view="presentation" hide-input="false" hide-output="true" inline-output="false" labelreference="L2291" drawlabel="true">
<Input>
<Text-field style="Text" layout="Normal"><Equation executable="false" style="2D Math" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2I1EhRicvJSxtYXRodmFyaWFudEdRJ25vcm1hbEYn">JSFH</Equation></Text-field>
</Input>
</Group></Presentation-Block>
</Section>
<Section collapsed="true" MultipleChoiceAnswerIndex="-1" MultipleChoiceRandomizeChoices="false" TrueFalseAnswerIndex="-1" EssayAnswerRows="5" EssayAnswerColumns="60"><Title>
<Text-field style="Heading 3" layout="Heading 3">4.2.2 Considerations on building a Benchmark Rate</Text-field></Title><Presentation-Block>
<Group view="presentation" hide-input="false" hide-output="true" inline-output="false" labelreference="L2339" drawlabel="true">
<Input>
<Text-field style="Text" layout="Normal"><Equation executable="false" style="2D Math" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2I1EhRicvJSxtYXRodmFyaWFudEdRJ25vcm1hbEYn">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=</Equation></Text-field>
</Input>
</Group></Presentation-Block><Table interior="group" showinput="true" alignment="left" exterior="all" width="90.42769857433808%" labelreference="L9608" showlabel="true" captionalignment="0" title="" order="row" drawcaption="false" randomized="false" captionposition="1" plotalignlists="" pagebreak="cell" postexecute="insert" showgroup="true"><Table-Column weight="1332" separator="true"></Table-Column><Table-Row align="top" separator="true"><Table-Cell columnspan="1" backgroundstyle="0" rowspan="1" padding="5" fillcolor="[255,255,255]"><Table interior="group" showinput="true" alignment="left" exterior="none" width="65.78411405295316%" labelreference="L9611" showlabel="true" captionalignment="0" order="row" drawcaption="false" randomized="false" captionposition="1" plotalignlists="" pagebreak="cell" postexecute="insert" showgroup="true"><Table-Column weight="214" separator="false"></Table-Column><Table-Column weight="49" separator="false"></Table-Column><Table-Column weight="706" separator="false"></Table-Column><Table-Row align="baseline" separator="false"><Table-Cell columnspan="1" backgroundstyle="0" rowspan="1" padding="5" fillcolor="[255,255,255]">
<Text-field style="Text" layout="Normal"><Font font_style_name="Help Fixed" superscript="false" placeholder="false" executable="false" selection-placeholder="false" italic="false" size="12" bold="false" style="Help Fixed" subscript="false" family="Times New Roman" opaque="false" underline="false" background="[255,255,255]" readonly="false" foreground="[0,0,0]">tenor</Font></Text-field></Table-Cell><Table-Cell columnspan="1" backgroundstyle="0" rowspan="1" padding="5" fillcolor="[255,255,255]">
<Text-field style="Text" layout="Normal"><Font font_style_name="Help Fixed" superscript="false" placeholder="false" executable="false" selection-placeholder="false" italic="false" size="12" bold="false" style="Help Fixed" subscript="false" family="Times New Roman" opaque="false" underline="false" background="[255,255,255]" readonly="false" foreground="[0,0,0]">-</Font></Text-field></Table-Cell><Table-Cell columnspan="1" backgroundstyle="0" rowspan="1" padding="5" fillcolor="[255,255,255]">
<Text-field style="Text" layout="Normal">positive integer; length of the tenor</Text-field></Table-Cell></Table-Row><Table-Row align="baseline" separator="false"><Table-Cell columnspan="1" backgroundstyle="0" rowspan="1" padding="5" fillcolor="[255,255,255]">
<Text-field style="Text" layout="Normal"><Font font_style_name="Help Fixed" superscript="false" placeholder="false" executable="false" selection-placeholder="false" italic="false" size="12" bold="false" style="Help Fixed" subscript="false" family="Times New Roman" opaque="false" underline="false" background="[255,255,255]" readonly="false" foreground="[0,0,0]">units</Font></Text-field></Table-Cell><Table-Cell columnspan="1" backgroundstyle="0" rowspan="1" padding="5" fillcolor="[255,255,255]">
<Text-field style="Text" layout="Normal"><Font font_style_name="Help Fixed" superscript="false" placeholder="false" executable="false" selection-placeholder="false" italic="false" size="12" bold="false" style="Help Fixed" subscript="false" family="Times New Roman" opaque="false" underline="false" background="[255,255,255]" readonly="false" foreground="[0,0,0]">-</Font></Text-field></Table-Cell><Table-Cell columnspan="1" backgroundstyle="0" rowspan="1" padding="5" fillcolor="[255,255,255]">
<Text-field style="Text" layout="Normal"><Font font_style_name="Help Maple Name" superscript="false" placeholder="false" executable="false" selection-placeholder="false" italic="false" size="12" bold="false" style="Help Maple Name" subscript="false" family="Times New Roman" opaque="false" underline="false" background="[255,255,255]" readonly="false" foreground="[0,0,0]">Days</Font>, <Font font_style_name="Help Maple Name" superscript="false" placeholder="false" executable="false" selection-placeholder="false" italic="false" size="12" bold="false" style="Help Maple Name" subscript="false" family="Times New Roman" opaque="false" underline="false" background="[255,255,255]" readonly="false" foreground="[0,0,0]">Weeks</Font>, <Font font_style_name="Help Maple Name" superscript="false" placeholder="false" executable="false" selection-placeholder="false" italic="false" size="12" bold="false" style="Help Maple Name" subscript="false" family="Times New Roman" opaque="false" underline="false" background="[255,255,255]" readonly="false" foreground="[0,0,0]">Months</Font>, or <Font font_style_name="Help Maple Name" superscript="false" placeholder="false" executable="false" selection-placeholder="false" italic="false" size="12" bold="false" style="Help Maple Name" subscript="false" family="Times New Roman" opaque="false" underline="false" background="[255,255,255]" readonly="false" foreground="[0,0,0]">Years</Font>; time units</Text-field></Table-Cell></Table-Row><Table-Row align="baseline" separator="false"><Table-Cell columnspan="1" backgroundstyle="0" rowspan="1" padding="5" fillcolor="[255,255,255]">
<Text-field style="Text" layout="Normal"><Font font_style_name="Help Fixed" superscript="false" placeholder="false" executable="false" selection-placeholder="false" italic="false" size="12" bold="false" style="Help Fixed" subscript="false" family="Times New Roman" opaque="false" underline="false" background="[255,255,255]" readonly="false" foreground="[0,0,0]">familyname</Font></Text-field></Table-Cell><Table-Cell columnspan="1" backgroundstyle="0" rowspan="1" padding="5" fillcolor="[255,255,255]">
<Text-field style="Text" layout="Normal"><Font font_style_name="Help Fixed" superscript="false" placeholder="false" executable="false" selection-placeholder="false" italic="false" size="12" bold="false" style="Help Fixed" subscript="false" family="Times New Roman" opaque="false" underline="false" background="[255,255,255]" readonly="false" foreground="[0,0,0]">-</Font></Text-field></Table-Cell><Table-Cell columnspan="1" backgroundstyle="0" rowspan="1" padding="5" fillcolor="[255,255,255]">
<Text-field style="Text" layout="Normal">family name; can be one of the following: <Font font_style_name="Help Maple Name" superscript="false" placeholder="false" executable="false" selection-placeholder="false" italic="false" size="12" bold="false" style="Help Maple Name" subscript="false" family="Times New Roman" opaque="false" underline="false" background="[255,255,255]" readonly="false" foreground="[0,0,0]">AUDLIBOR</Font>, <Font font_style_name="Help Maple Name" superscript="false" placeholder="false" executable="false" selection-placeholder="false" italic="false" size="12" bold="false" style="Help Maple Name" subscript="false" family="Times New Roman" opaque="false" underline="false" background="[255,255,255]" readonly="false" foreground="[0,0,0]">CADLIBOR</Font>, <Font font_style_name="Help Maple Name" superscript="false" placeholder="false" executable="false" selection-placeholder="false" italic="false" size="12" bold="false" style="Help Maple Name" subscript="false" family="Times New Roman" opaque="false" underline="false" background="[255,255,255]" readonly="false" foreground="[0,0,0]">CDOR</Font>, <Font font_style_name="Help Maple Name" superscript="false" placeholder="false" executable="false" selection-placeholder="false" italic="false" size="12" bold="false" style="Help Maple Name" subscript="false" family="Times New Roman" opaque="false" underline="false" background="[255,255,255]" readonly="false" foreground="[0,0,0]">CHFLIBOR</Font>, <Font font_style_name="Help Maple Name" superscript="false" placeholder="false" executable="false" selection-placeholder="false" italic="false" size="12" bold="false" style="Help Maple Name" subscript="false" family="Times New Roman" opaque="false" underline="false" background="[255,255,255]" readonly="false" foreground="[0,0,0]">DKKLIBOR</Font>, <Font font_style_name="Help Maple Name" superscript="false" placeholder="false" executable="false" selection-placeholder="false" italic="false" size="12" bold="false" style="Help Maple Name" subscript="false" family="Times New Roman" opaque="false" underline="false" background="[255,255,255]" readonly="false" foreground="[0,0,0]">EURIBOR</Font>, <Font font_style_name="Help Maple Name" superscript="false" placeholder="false" executable="false" selection-placeholder="false" italic="false" size="12" bold="false" style="Help Maple Name" subscript="false" family="Times New Roman" opaque="false" underline="false" background="[255,255,255]" readonly="false" foreground="[0,0,0]">GBPLIBOR</Font>, <Font font_style_name="Help Maple Name" superscript="false" placeholder="false" executable="false" selection-placeholder="false" italic="false" size="12" bold="false" style="Help Maple Name" subscript="false" family="Times New Roman" opaque="false" underline="false" background="[255,255,255]" readonly="false" foreground="[0,0,0]">JIBAR</Font>, <Font font_style_name="Help Maple Name" superscript="false" placeholder="false" executable="false" selection-placeholder="false" italic="false" size="12" bold="false" style="Help Maple Name" subscript="false" family="Times New Roman" opaque="false" underline="false" background="[255,255,255]" readonly="false" foreground="[0,0,0]">JPYLIBOR</Font>, <Font font_style_name="Help Maple Name" superscript="false" placeholder="false" executable="false" selection-placeholder="false" italic="false" size="12" bold="false" style="Help Maple Name" subscript="false" family="Times New Roman" opaque="false" underline="false" background="[255,255,255]" readonly="false" foreground="[0,0,0]">NZDLIBOR</Font>, <Font font_style_name="Help Maple Name" superscript="false" placeholder="false" executable="false" selection-placeholder="false" italic="false" size="12" bold="false" style="Help Maple Name" subscript="false" family="Times New Roman" opaque="false" underline="false" background="[255,255,255]" readonly="false" foreground="[0,0,0]">TIBOR</Font>, <Font font_style_name="Help Maple Name" superscript="false" placeholder="false" executable="false" selection-placeholder="false" italic="false" size="12" bold="false" style="Help Maple Name" subscript="false" family="Times New Roman" opaque="false" underline="false" background="[255,255,255]" readonly="false" foreground="[0,0,0]">TRLIBOR</Font>, <Font font_style_name="Help Maple Name" superscript="false" placeholder="false" executable="false" selection-placeholder="false" italic="false" size="12" bold="false" style="Help Maple Name" subscript="false" family="Times New Roman" opaque="false" underline="false" background="[255,255,255]" readonly="false" foreground="[0,0,0]">USDLIBOR</Font>, <Font font_style_name="Help Maple Name" superscript="false" placeholder="false" executable="false" selection-placeholder="false" italic="false" size="12" bold="false" style="Help Maple Name" subscript="false" family="Times New Roman" opaque="false" underline="false" background="[255,255,255]" readonly="false" foreground="[0,0,0]">ZIBOR</Font></Text-field></Table-Cell></Table-Row><Table-Row align="baseline" separator="false"><Table-Cell columnspan="1" backgroundstyle="0" rowspan="1" padding="5" fillcolor="[255,255,255]">
<Text-field style="Text" layout="Normal"><Font font_style_name="Help Fixed" superscript="false" placeholder="false" executable="false" selection-placeholder="false" italic="false" size="12" bold="false" style="Help Fixed" subscript="false" family="Times New Roman" opaque="false" underline="false" background="[255,255,255]" readonly="false" foreground="[0,0,0]">forecast</Font></Text-field></Table-Cell><Table-Cell columnspan="1" backgroundstyle="0" rowspan="1" padding="5" fillcolor="[255,255,255]">
<Text-field style="Text" layout="Normal"><Font font_style_name="Help Fixed" superscript="false" placeholder="false" executable="false" selection-placeholder="false" italic="false" size="12" bold="false" style="Help Fixed" subscript="false" family="Times New Roman" opaque="false" underline="false" background="[255,255,255]" readonly="false" foreground="[0,0,0]">-</Font></Text-field></Table-Cell><Table-Cell columnspan="1" backgroundstyle="0" rowspan="1" padding="5" fillcolor="[255,255,255]">
<Text-field style="Text" layout="Normal">yield term structure; forecasted rate or term structure</Text-field></Table-Cell></Table-Row></Table><Presentation-Block>
<Group view="presentation" hide-input="false" hide-output="true" inline-output="false" labelreference="L9609" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input>
<Text-field style="Text" layout="Normal"></Text-field>
</Input>
</Group></Presentation-Block></Table-Cell></Table-Row></Table><Presentation-Block>
<Group view="presentation" hide-input="false" hide-output="true" inline-output="false" labelreference="L2340" drawlabel="true">
<Input>
<Text-field style="Text" layout="Normal"></Text-field>
</Input>
</Group></Presentation-Block>
</Section>
<Section collapsed="true" MultipleChoiceAnswerIndex="-1" MultipleChoiceRandomizeChoices="false" TrueFalseAnswerIndex="-1" EssayAnswerRows="5" EssayAnswerColumns="60"><Title>
<Text-field style="Heading 3" layout="Heading 3">4.2.1 Building and Valuing a Swaption</Text-field></Title>
<Section collapsed="true" MultipleChoiceAnswerIndex="-1" MultipleChoiceRandomizeChoices="false" TrueFalseAnswerIndex="-1" EssayAnswerRows="5" EssayAnswerColumns="60"><Title>
<Text-field style="Heading 4" layout="Heading 4">4.2.1.1 Some considerations behind the parametrization of the Hull White Model</Text-field></Title><Presentation-Block>
<Group view="presentation" hide-input="false" hide-output="true" inline-output="false" labelreference="L2564" drawlabel="true">
<Input>
<Text-field style="Text" layout="Normal"></Text-field>
</Input>
</Group></Presentation-Block><Table interior="group" showinput="true" alignment="left" exterior="all" width="90.3939184519696%" labelreference="L9613" showlabel="true" captionalignment="0" title="" order="row" drawcaption="false" randomized="false" captionposition="1" plotalignlists="" pagebreak="cell" postexecute="insert" showgroup="true"><Table-Column weight="1308" separator="true"></Table-Column><Table-Row align="top" separator="true"><Table-Cell columnspan="1" backgroundstyle="0" rowspan="1" padding="5" fillcolor="[255,255,255]"><Presentation-Block>
<Group view="presentation" hide-input="false" hide-output="true" inline-output="false" labelreference="L9616" drawlabel="true">
<Input>
<Text-field style="Text" layout="Normal">We decided to use the Hull White algorithm because it can handle term strutures directly.</Text-field>
</Input>
</Group></Presentation-Block><Presentation-Block>
<Group view="presentation" hide-input="false" hide-output="true" inline-output="false" labelreference="L9615" drawlabel="true">
<Input>
<Text-field style="Text" layout="Normal">We can think of other alternatives like the one designed inthe interesr rate swap section.</Text-field>
</Input>
</Group></Presentation-Block><Presentation-Block>
<Group view="presentation" hide-input="false" hide-output="true" inline-output="false" labelreference="L9618" drawlabel="true">
<Input>
<Text-field style="Text" layout="Normal">We will take  a forward curve that will have certain volatility around. This is reset at each node and a short term process is produced.</Text-field>
</Input>
</Group></Presentation-Block><Presentation-Block>
<Group view="presentation" hide-input="false" hide-output="true" inline-output="false" labelreference="L9617" drawlabel="true">
<Input>
<Text-field style="Text" layout="Normal">We will input a Forward Rate but for the purpose of writing the code we will foolmaple into thinking that is forward rate thespite that we will use the code of a zero rate.</Text-field>
</Input>
</Group></Presentation-Block><Presentation-Block>
<Group view="presentation" hide-input="false" hide-output="true" inline-output="false" labelreference="L9614" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input>
<Text-field style="Text" layout="Normal"></Text-field>
</Input>
</Group></Presentation-Block></Table-Cell></Table-Row></Table><Presentation-Block>
<Group view="presentation" hide-input="false" hide-output="true" inline-output="false" labelreference="L2565" drawlabel="true">
<Input>
<Text-field style="Text" layout="Normal"><Equation executable="false" style="2D Math" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2I1EhRicvJSxtYXRodmFyaWFudEdRJ25vcm1hbEYn">JSFH</Equation></Text-field>
</Input>
</Group></Presentation-Block>
</Section>
<Section collapsed="true" MultipleChoiceAnswerIndex="-1" MultipleChoiceRandomizeChoices="false" TrueFalseAnswerIndex="-1" EssayAnswerRows="5" EssayAnswerColumns="60"><Title>
<Text-field style="Heading 4" layout="Heading 4">4.2.1.1  A Maple based Swap builder.</Text-field></Title><Presentation-Block>
<Group view="presentation" hide-input="false" hide-output="true" inline-output="false" labelreference="L2443" drawlabel="true">
<Input>
<Text-field style="Text" layout="Normal"><Equation executable="false" style="2D Math" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2I1EhRicvJSxtYXRodmFyaWFudEdRJ25vcm1hbEYn">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=</Equation><Equation executable="true" style="2D Input" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2I1EhRicvJStleGVjdXRhYmxlR1EmZmFsc2VGJy8lLG1hdGh2YXJpYW50R1Enbm9ybWFsRic=">JSFH</Equation></Text-field>
</Input>
</Group></Presentation-Block><Presentation-Block>
<Group view="presentation" hide-input="false" hide-output="true" inline-output="false" labelreference="L9259" drawlabel="true">
<Input>
<Text-field style="Text" layout="Normal"><Equation executable="true" style="2D Input" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2I1EhRicvJStleGVjdXRhYmxlR1EmZmFsc2VGJy8lLG1hdGh2YXJpYW50R1Enbm9ybWFsRic=">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=</Equation><EC-Button id="Button19" caption="Start" pixel-width="300" pixel-height="200" enabled="true" visible="true" show-border="true" user-size="false"><MapleCode action="click-event-handler">use DocumentTools in 
restart:
SetProperty(Button8, enabled, &quot;false&quot;):
SetProperty(Button10, enabled, &quot;false&quot;):
SetProperty(Button11, enabled, &quot;false&quot;):
SetProperty(Button13, enabled, &quot;false&quot;):
SetProperty(Button14, enabled, &quot;false&quot;):
SetProperty(Button18, enabled, &quot;false&quot;):
SetProperty(Button15, enabled, &quot;false&quot;):

SetProperty(Button12, enabled, &quot;true&quot;):
SetProperty(Button17, enabled, &quot;false&quot;):
end use; 
</MapleCode></EC-Button></Text-field>
</Input>
</Group></Presentation-Block><Table interior="group" showinput="true" alignment="left" exterior="all" width="71.83098591549296%" labelreference="L2307" showlabel="true" captionalignment="0" title="" order="row" drawcaption="false" randomized="false" captionposition="1" plotalignlists="" pagebreak="cell" postexecute="insert" showgroup="true"><Table-Column weight="212" separator="true"></Table-Column><Table-Column weight="553" separator="true"></Table-Column><Table-Row align="top" separator="true"><Table-Cell columnspan="1" backgroundstyle="1" rowspan="1" padding="5" fillcolor="[204,255,255]"><Presentation-Block>
<Group view="presentation" hide-input="false" hide-output="true" inline-output="false" labelreference="L2308" drawlabel="true">
<Input>
<Text-field style="Text" layout="Normal"></Text-field>
</Input>
</Group></Presentation-Block></Table-Cell><Table-Cell columnspan="1" backgroundstyle="1" italic="false" rowspan="1" padding="5" fillcolor="[204,255,255]"><Presentation-Block>
<Group view="presentation" hide-input="false" hide-output="true" inline-output="false" labelreference="L2309" drawlabel="true" redirect-target="L9336">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal" alignment="centred"><Font bold="true" style="Text" size="14">Swap Builder
Pay Fixed, Receive Float</Font></Text-field>
</Input>
<Output>
<Text-field superscript="false" placeholder="false" executable="false" selection-placeholder="false" italic="false" size="12" bold="false" subscript="false" family="Times New Roman" opaque="false" underline="false" background="[255,255,255]" readonly="false" foreground="[0,0,0]" alignment="centred" firstindent="0" spacebelow="0" leftmargin="0" linespacing="0.0" initial="0" linebreak="space" rightmargin="0" bulletsuffix="" spaceabove="0" bullet="none" pagebreak-before="false"><Equation executable="false" style="2D Output" display="LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVE1b3V0cHV0fnJlZGlyZWN0ZWQuLi5GJy8lJ2l0YWxpY0dRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJ25vcm1hbEYn">LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVE1b3V0cHV0fnJlZGlyZWN0ZWQuLi5GJy8lJ2l0YWxpY0dRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJ25vcm1hbEYn</Equation></Text-field>
</Output>
</Group></Presentation-Block><Presentation-Block>
<Group view="presentation" hide-input="false" hide-output="true" inline-output="false" labelreference="L9337" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal" alignment="centred"><Equation executable="true" style="2D Input" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2I1EhRicvJStleGVjdXRhYmxlR1EmZmFsc2VGJy8lLG1hdGh2YXJpYW50R1Enbm9ybWFsRic=">JSFH</Equation></Text-field>
</Input>
</Group></Presentation-Block></Table-Cell></Table-Row><Table-Row align="top" separator="true"><Table-Cell columnspan="1" backgroundstyle="0" rowspan="1" padding="5" fillcolor="[255,255,255]"><Presentation-Block>
<Group view="presentation" hide-input="false" hide-output="true" inline-output="false" labelreference="L2310" drawlabel="true">
<Input>
<Text-field style="Text" layout="Normal"><Font italic="true">Calendar Tools</Font></Text-field>
</Input>
</Group></Presentation-Block></Table-Cell><Table-Cell columnspan="1" backgroundstyle="0" rowspan="1" padding="5" fillcolor="[255,255,255]"><Presentation-Block>
<Group view="presentation" hide-input="false" hide-output="true" inline-output="false" labelreference="L2331" drawlabel="true">
<Input>
<Text-field style="Text" layout="Normal" alignment="centred"><Font italic="true">Calendar Convention</Font></Text-field>
</Input>
</Group></Presentation-Block><Presentation-Block>
<Group view="presentation" hide-input="false" hide-output="true" inline-output="false" labelreference="L2324" drawlabel="true">
<Input>
<Text-field style="Text" layout="Normal" alignment="centred">
<EC-RadioButton id="RadioButton7" groupname="Group2" caption="ISMA" enabled="true" visible="true" selected="true"></EC-RadioButton><EC-RadioButton id="RadioButton8" groupname="Group2" caption="ISDA" enabled="true" visible="true" selected="false"></EC-RadioButton><EC-RadioButton id="RadioButton9" groupname="Group2" caption="360" enabled="true" visible="true" selected="false"></EC-RadioButton><EC-RadioButton id="RadioButton10" groupname="Group2" caption="365" enabled="true" visible="true" selected="false"></EC-RadioButton></Text-field>
</Input>
</Group></Presentation-Block><Presentation-Block>
<Group view="presentation" hide-input="false" hide-output="true" inline-output="false" labelreference="L2336" drawlabel="true">
<Input>
<Text-field style="Text" layout="Normal" alignment="centred"></Text-field>
</Input>
</Group></Presentation-Block><Presentation-Block>
<Group view="presentation" hide-input="false" hide-output="true" inline-output="false" labelreference="L2323" drawlabel="true">
<Input>
<Text-field style="Text" layout="Normal"><Font italic="true">Evaluation Date   <EC-TextArea id="TextArea33" enabled="true" visible="true" visiblecharacterwidth="20" visiblerows="1" contents="&quot;June 1, 2014&quot;" editable="true" wrapping="true" show-border="true" password="false"></EC-TextArea> </Font></Text-field>
</Input>
</Group></Presentation-Block><Presentation-Block>
<Group view="presentation" hide-input="false" hide-output="true" inline-output="false" labelreference="L2335" drawlabel="true">
<Input>
<Text-field style="Text" italic="true" layout="Normal"><Font italic="true">Start  Date           <EC-TextArea id="TextArea34" enabled="true" visible="true" visiblecharacterwidth="20" visiblerows="1" contents="&quot;June 1, 2015&quot;" editable="true" wrapping="true" show-border="true" password="false"></EC-TextArea> </Font></Text-field>
</Input>
</Group></Presentation-Block><Presentation-Block>
<Group view="presentation" hide-input="false" hide-output="true" inline-output="false" labelreference="L2325" drawlabel="true">
<Input>
<Text-field style="Text" italic="true" layout="Normal"><Font italic="true">Maturity Date      <EC-TextArea id="TextArea35" enabled="true" visible="true" visiblecharacterwidth="20" visiblerows="1" contents="&quot;June 1, 2030&quot;" editable="true" wrapping="true" show-border="true" password="false"></EC-TextArea> </Font></Text-field>
</Input>
</Group></Presentation-Block><Presentation-Block>
<Group view="presentation" hide-input="false" hide-output="true" inline-output="false" labelreference="L2326" drawlabel="true">
<Input>
<Text-field style="Text" italic="true" layout="Normal" alignment="centred"></Text-field>
</Input>
</Group></Presentation-Block><Presentation-Block>
<Group view="presentation" hide-input="false" hide-output="true" inline-output="false" labelreference="L2315" drawlabel="true">
<Input>
<Text-field style="Text" layout="Normal"><EC-Button id="Button12" caption="Set" pixel-width="300" pixel-height="200" enabled="true" visible="true" show-border="true" user-size="false"><MapleCode action="click-event-handler">use DocumentTools, Finance in 

# PART 1. OBTAINING THE CALENDAR CONVENTION

Do(a1=DocumentTools[GetProperty]('RadioButton7','value')):
Do(b1=DocumentTools[GetProperty]('RadioButton8','value')):
Do(c1=DocumentTools[GetProperty]('RadioButton9','value')):
Do(d1=DocumentTools[GetProperty]('RadioButton10','value')):

if a1=&quot;true&quot; then
	Do(f=1);
	elif b1=&quot;true&quot; then 
	Do(f=2);
	elif c1=&quot;true&quot; then
	Do(f=3);
	elif d1=&quot;true&quot; then 
	Do(f=4);
end if;
		
if f=1 then
	Do(h=Finance[DayCounter](Actual365Fixed)):
	elif f=2 then 
	Do(h=Finance[DayCounter](Actual365Fixed)):
	elif f=3 then
	Do(h=Finance[DayCounter](ISDA)):
	elif f=4 then 
	Do(h=Finance[DayCounter](Actual360)):
end if;



Do(SetEvaluationDate(%TextArea33)):
Do(start=%TextArea34):
Do(maturity=%TextArea35):
SetProperty(Button10, enabled, &quot;true&quot;):

end use; 


</MapleCode></EC-Button></Text-field>
</Input>
</Group></Presentation-Block></Table-Cell></Table-Row><Table-Row align="top" separator="true"><Table-Cell columnspan="1" backgroundstyle="0" rowspan="1" padding="5" fillcolor="[255,255,255]"><Presentation-Block>
<Group view="presentation" hide-input="false" hide-output="true" inline-output="false" labelreference="L2353" drawlabel="true">
<Input>
<Text-field style="Text" layout="Normal"><Equation executable="false" style="2D Math" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYqLUkjbWlHRiQ2JVEmRml4ZWRGJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRictSSNtb0dGJDYuUSJ+RidGL0YyLyUmZmVuY2VHUSZmYWxzZUYnLyUqc2VwYXJhdG9yR0Y7LyUpc3RyZXRjaHlHRjsvJSpzeW1tZXRyaWNHRjsvJShsYXJnZW9wR0Y7LyUubW92YWJsZWxpbWl0c0dGOy8lJ2FjY2VudEdGOy8lJ2xzcGFjZUdRJjAuMGVtRicvJSdyc3BhY2VHRkpGNS1GLDYlUSRMZWdGJ0YvRjJGNS1GLDYlUSlTY2hlZHVsZUYnRi9GMkYvRjI=">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYqLUkjbWlHRiQ2JVEmRml4ZWRGJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRictSSNtb0dGJDYuUSJ+RidGL0YyLyUmZmVuY2VHUSZmYWxzZUYnLyUqc2VwYXJhdG9yR0Y7LyUpc3RyZXRjaHlHRjsvJSpzeW1tZXRyaWNHRjsvJShsYXJnZW9wR0Y7LyUubW92YWJsZWxpbWl0c0dGOy8lJ2FjY2VudEdGOy8lJ2xzcGFjZUdRJjAuMGVtRicvJSdyc3BhY2VHRkpGNS1GLDYlUSRMZWdGJ0YvRjJGNS1GLDYlUSlTY2hlZHVsZUYnRi9GMkYvRjI=</Equation></Text-field>
</Input>
</Group></Presentation-Block></Table-Cell><Table-Cell columnspan="1" backgroundstyle="0" rowspan="1" padding="5" fillcolor="[255,255,255]"><Presentation-Block>
<Group view="presentation" hide-input="false" hide-output="true" inline-output="false" labelreference="L2354" drawlabel="true">
<Input>
<Text-field style="Text" italic="true" layout="Normal"><Font italic="true">Frequency                          <EC-RadioButton id="RadioButton14" groupname="Group0" caption="Annual" enabled="true" visible="true" selected="true"></EC-RadioButton><EC-RadioButton id="RadioButton15" groupname="Group0" caption="Semi Annual" enabled="true" visible="true" selected="false"></EC-RadioButton><EC-RadioButton id="RadioButton16" groupname="Group0" caption="Quarterly" enabled="true" visible="true" selected="false"></EC-RadioButton><EC-RadioButton id="RadioButton17" groupname="Group0" caption="Monthly" enabled="true" visible="true" selected="false"></EC-RadioButton></Font></Text-field>
</Input>
</Group></Presentation-Block><Presentation-Block>
<Group view="presentation" hide-input="false" hide-output="true" inline-output="false" labelreference="L2357" drawlabel="true">
<Input>
<Text-field style="Text" italic="true" layout="Normal"><Font italic="true">Calendar                            <EC-RadioButton id="RadioButton18" groupname="Group1" caption="USD LIBOR" enabled="true" visible="true" selected="false"></EC-RadioButton><EC-RadioButton id="RadioButton19" groupname="Group1" caption="EURIBOR" enabled="true" visible="true" selected="true"></EC-RadioButton><EC-RadioButton id="RadioButton20" groupname="Group1" caption="GBP LIBOR" enabled="true" visible="true" selected="false"></EC-RadioButton></Font></Text-field>
</Input>
</Group></Presentation-Block><Presentation-Block>
<Group view="presentation" hide-input="false" hide-output="true" inline-output="false" labelreference="L2397" drawlabel="true">
<Input>
<Text-field style="Text" layout="Normal"></Text-field>
</Input>
</Group></Presentation-Block><Presentation-Block>
<Group view="presentation" hide-input="false" hide-output="true" inline-output="false" labelreference="L2381" drawlabel="true">
<Input>
<Text-field style="Text" layout="Normal"><EC-Button id="Button10" caption="Set" pixel-width="300" pixel-height="200" enabled="true" visible="true" show-border="true" user-size="false"><MapleCode action="click-event-handler">use DocumentTools, Finance in 
# PART 2. SETTING THE PAYING LEG

Do(a2=DocumentTools[GetProperty]('RadioButton14','value')):
Do(b2=DocumentTools[GetProperty]('RadioButton15','value')):
Do(c2=DocumentTools[GetProperty]('RadioButton16','value')):
Do(d2=DocumentTools[GetProperty]('RadioButton17','value')):

if a2=&quot;true&quot; then
	Do(f2=Annual);
	elif b2=&quot;true&quot; then 
	Do(f2=Semiannual);
	elif c2=&quot;true&quot; then
	Do(f2=Quarterly);
	elif d2=&quot;true&quot; then 
	Do(f2=Monthly);
end if;


Do(a3=DocumentTools[GetProperty]('RadioButton14','value')):
Do(b3=DocumentTools[GetProperty]('RadioButton15','value')):
Do(c3=DocumentTools[GetProperty]('RadioButton16','value')):

if a3=&quot;true&quot; then
	Do(f3=USDLIBOR);
	elif b3=&quot;true&quot; then 
	Do(f3=EURIBOR);
	elif c3=&quot;true&quot; then
	Do(f3=GBPLIBOR);
end if;
	
Do(Sch1=Schedule(start, maturity, f2, 'calendar'=f3)):	
SetProperty(Button11, enabled, &quot;true&quot;):
end use; 
</MapleCode></EC-Button></Text-field>
</Input>
</Group></Presentation-Block></Table-Cell></Table-Row><Table-Row align="top" separator="true"><Table-Cell columnspan="1" backgroundstyle="0" rowspan="1" padding="5" fillcolor="[255,255,255]"><Presentation-Block>
<Group view="presentation" hide-input="false" hide-output="true" inline-output="false" labelreference="L2355" drawlabel="true">
<Input>
<Text-field style="Text" layout="Normal"><Font italic="true">Flexible Leg Schedule</Font></Text-field>
</Input>
</Group></Presentation-Block></Table-Cell><Table-Cell columnspan="1" backgroundstyle="0" rowspan="1" padding="5" fillcolor="[255,255,255]"><Presentation-Block>
<Group view="presentation" hide-input="false" hide-output="true" inline-output="false" labelreference="L2380" drawlabel="true">
<Input>
<Text-field style="Text" italic="true" layout="Normal"><Font italic="true">Frequency                          <EC-RadioButton id="RadioButton21" groupname="Group3" caption="Annual" enabled="true" visible="true" selected="false"></EC-RadioButton><EC-RadioButton id="RadioButton22" groupname="Group3" caption="Semi Annual" enabled="true" visible="true" selected="false"></EC-RadioButton><EC-RadioButton id="RadioButton23" groupname="Group3" caption="Quarterly" enabled="true" visible="true" selected="true"></EC-RadioButton><EC-RadioButton id="RadioButton24" groupname="Group3" caption="Monthly" enabled="true" visible="true" selected="false"></EC-RadioButton></Font></Text-field>
</Input>
</Group></Presentation-Block><Presentation-Block>
<Group view="presentation" hide-input="false" hide-output="true" inline-output="false" labelreference="L2379" drawlabel="true">
<Input>
<Text-field style="Text" italic="true" layout="Normal"><Font italic="true">Calendar                            <EC-RadioButton id="RadioButton25" groupname="Group4" caption="USD LIBOR" enabled="true" visible="true" selected="false"></EC-RadioButton><EC-RadioButton id="RadioButton26" groupname="Group4" caption="EURIBOR" enabled="true" visible="true" selected="true"></EC-RadioButton><EC-RadioButton id="RadioButton27" groupname="Group4" caption="GBP LIBOR" enabled="true" visible="true" selected="false"></EC-RadioButton></Font></Text-field>
</Input>
</Group></Presentation-Block><Presentation-Block>
<Group view="presentation" hide-input="false" hide-output="true" inline-output="false" labelreference="L2399" drawlabel="true">
<Input>
<Text-field style="Text" layout="Normal"><Equation executable="false" style="2D Math" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2I1EhRicvJSxtYXRodmFyaWFudEdRJ25vcm1hbEYn">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=</Equation></Text-field>
</Input>
</Group></Presentation-Block><Presentation-Block>
<Group view="presentation" hide-input="false" hide-output="true" inline-output="false" labelreference="L2356" drawlabel="true">
<Input>
<Text-field style="Text" layout="Normal"><EC-Button id="Button11" caption="Set" pixel-width="300" pixel-height="200" enabled="true" visible="true" show-border="true" user-size="false"><MapleCode action="click-event-handler">
use DocumentTools, Finance in 
# PART 2. SETTING THE PAYING LEG

Do(a4=DocumentTools[GetProperty]('RadioButton21','value')):
Do(b4=DocumentTools[GetProperty]('RadioButton22','value')):
Do(c4=DocumentTools[GetProperty]('RadioButton23','value')):
Do(d4=DocumentTools[GetProperty]('RadioButton24','value')):

if a4=&quot;true&quot; then
	Do(f4=Annual);
	elif b4=&quot;true&quot; then 
	Do(f4=Semiannual);
	elif c4=&quot;true&quot; then
	Do(f4=Quarterly);
	elif d4=&quot;true&quot; then 
	Do(f4=Monthly);
end if;


Do(a5=DocumentTools[GetProperty]('RadioButton25','value')):
Do(b5=DocumentTools[GetProperty]('RadioButton26','value')):
Do(c5=DocumentTools[GetProperty]('RadioButton27','value')):

if a5=&quot;true&quot; then
	Do(f5=USDLIBOR);
	elif b5=&quot;true&quot; then 
	Do(f5=EURIBOR);
	elif c5=&quot;true&quot; then
	Do(f5=GBPLIBOR);
end if;
	
Do(Sch2=Schedule(start, maturity, f4, 'calendar'=f5)):	
SetProperty(Button13, enabled, &quot;true&quot;):
end use; 

</MapleCode></EC-Button></Text-field>
</Input>
</Group></Presentation-Block></Table-Cell></Table-Row><Table-Row align="top" separator="true"><Table-Cell columnspan="1" backgroundstyle="0" rowspan="1" padding="5" fillcolor="[255,255,255]"><Presentation-Block>
<Group view="presentation" hide-input="false" hide-output="true" inline-output="false" labelreference="L2312" drawlabel="true">
<Input>
<Text-field style="Text" layout="Normal"><Font italic="true">Forward Curve Builder</Font></Text-field>
</Input>
</Group></Presentation-Block></Table-Cell><Table-Cell columnspan="1" backgroundstyle="0" rowspan="1" padding="5" fillcolor="[255,255,255]"><Presentation-Block>
<Group view="presentation" hide-input="false" hide-output="true" inline-output="false" labelreference="L2392" drawlabel="true">
<Input>
<Text-field style="Text" layout="Normal" alignment="centred"><Font italic="true">Rates</Font></Text-field>
</Input>
</Group></Presentation-Block><Presentation-Block>
<Group view="presentation" hide-input="false" hide-output="true" inline-output="false" labelreference="L2418" drawlabel="true">
<Input>
<Text-field style="Text" layout="Normal" alignment="centred"><EC-MathContainer id="MathContainer11" pixel-width="300" pixel-height="75" expression="&lt;math xmlns='http://www.w3.org/1998/Math/MathML'&gt;&lt;mstyle fontfamily='Times New Roman' mathsize='12pt' mathcolor='#000000'  veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.7099999785423279' scriptminsize='8.0pt'&gt;&lt;mrow&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mrow&gt;&lt;mfenced open='[' close=']' separators=','&gt;&lt;mrow&gt;&lt;mn fontweight='normal'&gt;0.04875825&lt;/mn&gt;&lt;mo fontweight='normal' separator='true' lspace='0.0em' rspace='0.3333333em'&gt;&amp;comma;&lt;/mo&gt;&lt;mn fontweight='normal'&gt;0.04875825&lt;/mn&gt;&lt;mo fontweight='normal' separator='true' lspace='0.0em' rspace='0.3333333em'&gt;&amp;comma;&lt;/mo&gt;&lt;mn fontweight='normal'&gt;0.04875825&lt;/mn&gt;&lt;mo fontweight='normal' separator='true' lspace='0.0em' rspace='0.3333333em'&gt;&amp;comma;&lt;/mo&gt;&lt;mn fontweight='normal'&gt;0.04875825&lt;/mn&gt;&lt;mo fontweight='normal' separator='true' lspace='0.0em' rspace='0.3333333em'&gt;&amp;comma;&lt;/mo&gt;&lt;mn fontweight='normal'&gt;0.04875825&lt;/mn&gt;&lt;mo fontweight='normal' separator='true' lspace='0.0em' rspace='0.3333333em'&gt;&amp;comma;&lt;/mo&gt;&lt;mn fontweight='normal'&gt;0.04875825&lt;/mn&gt;&lt;mo fontweight='normal' separator='true' lspace='0.0em' rspace='0.3333333em'&gt;&amp;comma;&lt;/mo&gt;&lt;mn fontweight='normal'&gt;0.04875825&lt;/mn&gt;&lt;mo fontweight='normal' separator='true' lspace='0.0em' rspace='0.3333333em'&gt;&amp;comma;&lt;/mo&gt;&lt;mn fontweight='normal'&gt;0.04875825&lt;/mn&gt;&lt;/mrow&gt;&lt;/mfenced&gt;&lt;/mrow&gt;&lt;/mrow&gt;&lt;/mstyle&gt;&lt;/math&gt;" visible="true" show-border="true" autofit="false"></EC-MathContainer></Text-field>
</Input>
</Group></Presentation-Block><Presentation-Block>
<Group view="presentation" hide-input="false" hide-output="true" inline-output="false" labelreference="L2420" drawlabel="true">
<Input>
<Text-field style="Text" layout="Normal" alignment="centred"></Text-field>
</Input>
</Group></Presentation-Block><Presentation-Block>
<Group view="presentation" hide-input="false" hide-output="true" inline-output="false" labelreference="L2351" drawlabel="true">
<Input>
<Text-field style="Text" layout="Normal" alignment="centred"><Font italic="true">Times</Font></Text-field>
</Input>
</Group></Presentation-Block><Presentation-Block>
<Group view="presentation" hide-input="false" hide-output="true" inline-output="false" labelreference="L2352" drawlabel="true">
<Input>
<Text-field style="Text" layout="Normal" alignment="centred"><EC-MathContainer id="MathContainer12" pixel-width="300" pixel-height="75" expression="&lt;math xmlns='http://www.w3.org/1998/Math/MathML'&gt;&lt;mstyle fontfamily='Times New Roman' mathsize='12pt' mathcolor='#000000'  veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.7099999785423279' scriptminsize='8.0pt'&gt;&lt;mrow&gt;&lt;mi mathvariant='normal' fontweight='normal'&gt;&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mfenced open='[' close=']' separators=','&gt;&lt;mrow&gt;&lt;mn fontweight='normal'&gt;0.0&lt;/mn&gt;&lt;mo fontweight='normal' separator='true' lspace='0.0em' rspace='0.3333333em'&gt;&amp;comma;&lt;/mo&gt;&lt;mn fontweight='normal'&gt;0.5&lt;/mn&gt;&lt;mo fontweight='normal' separator='true' lspace='0.0em' rspace='0.3333333em'&gt;&amp;comma;&lt;/mo&gt;&lt;mspace height='0.0ex' width='1.0em' depth='0.0ex' linebreak='nobreak'/&gt;&lt;mn fontweight='normal'&gt;1&lt;/mn&gt;&lt;mo fontweight='normal' separator='true' lspace='0.0em' rspace='0.3333333em'&gt;&amp;comma;&lt;/mo&gt;&lt;mspace height='0.0ex' width='1.0em' depth='0.0ex' linebreak='nobreak'/&gt;&lt;mn fontweight='normal'&gt;3&lt;/mn&gt;&lt;mo fontweight='normal' separator='true' lspace='0.0em' rspace='0.3333333em'&gt;&amp;comma;&lt;/mo&gt;&lt;mspace height='0.0ex' width='1.0em' depth='0.0ex' linebreak='nobreak'/&gt;&lt;mn fontweight='normal'&gt;5&lt;/mn&gt;&lt;mo fontweight='normal' separator='true' lspace='0.0em' rspace='0.3333333em'&gt;&amp;comma;&lt;/mo&gt;&lt;mspace height='0.0ex' width='1.0em' depth='0.0ex' linebreak='nobreak'/&gt;&lt;mn fontweight='normal'&gt;7&lt;/mn&gt;&lt;mo fontweight='normal' separator='true' lspace='0.0em' rspace='0.3333333em'&gt;&amp;comma;&lt;/mo&gt;&lt;mn fontweight='normal'&gt;10&lt;/mn&gt;&lt;mo fontweight='normal' separator='true' lspace='0.0em' rspace='0.3333333em'&gt;&amp;comma;&lt;/mo&gt;&lt;mspace height='0.0ex' width='1.0em' depth='0.0ex' linebreak='nobreak'/&gt;&lt;mn fontweight='normal'&gt;30&lt;/mn&gt;&lt;/mrow&gt;&lt;/mfenced&gt;&lt;/mrow&gt;&lt;/mstyle&gt;&lt;/math&gt;" visible="true" show-border="true" autofit="false"></EC-MathContainer></Text-field>
</Input>
</Group></Presentation-Block><Presentation-Block>
<Group view="presentation" hide-input="false" hide-output="true" inline-output="false" labelreference="L2346" drawlabel="true">
<Input>
<Text-field style="Text" layout="Normal"><EC-Button id="Button13" caption="Set" pixel-width="300" pixel-height="200" enabled="true" visible="true" show-border="true" user-size="false"><MapleCode action="click-event-handler">use DocumentTools, Finance in 

Do(rates=%MathContainer11):
Do(times=%MathContainer12):

if f=1 then
	Do(h1=Actual365Fixed):
	elif f=2 then 
	Do(h1=Actual365Fixed):
	elif f=3 then
	Do(h1=ISDA):
	elif f=4 then 
	Do(h1=Actual360):
end if;





Do(discount_curve = ZeroCurve(times,rates,'daycounter' = h1)):
SetProperty(Button14, enabled, &quot;true&quot;):
end use; 
</MapleCode></EC-Button></Text-field>
</Input>
</Group></Presentation-Block></Table-Cell></Table-Row><Table-Row align="top" separator="true"><Table-Cell columnspan="1" backgroundstyle="0" rowspan="1" padding="5" fillcolor="[255,255,255]"><Presentation-Block>
<Group view="presentation" hide-input="false" hide-output="true" inline-output="false" labelreference="L2348" drawlabel="true">
<Input>
<Text-field style="Text" layout="Normal"><Equation executable="false" style="2D Math" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYoLUkjbWlHRiQ2JVEqQmVuY2htYXJrRicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUkjbW9HRiQ2LVEifkYnL0YzUSdub3JtYWxGJy8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGPS8lKXN0cmV0Y2h5R0Y9LyUqc3ltbWV0cmljR0Y9LyUobGFyZ2VvcEdGPS8lLm1vdmFibGVsaW1pdHNHRj0vJSdhY2NlbnRHRj0vJSdsc3BhY2VHUSYwLjBlbUYnLyUncnNwYWNlR0ZMLUYsNiVRJVJhdGVGJ0YvRjJGNS1GLDYlUShCdWlsZGVyRidGL0YyRjk=">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYoLUkjbWlHRiQ2JVEqQmVuY2htYXJrRicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUkjbW9HRiQ2LVEifkYnL0YzUSdub3JtYWxGJy8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGPS8lKXN0cmV0Y2h5R0Y9LyUqc3ltbWV0cmljR0Y9LyUobGFyZ2VvcEdGPS8lLm1vdmFibGVsaW1pdHNHRj0vJSdhY2NlbnRHRj0vJSdsc3BhY2VHUSYwLjBlbUYnLyUncnNwYWNlR0ZMLUYsNiVRJVJhdGVGJ0YvRjJGNS1GLDYlUShCdWlsZGVyRidGL0YyRjk=</Equation></Text-field>
</Input>
</Group></Presentation-Block></Table-Cell><Table-Cell columnspan="1" backgroundstyle="0" rowspan="1" padding="5" fillcolor="[255,255,255]"><Presentation-Block>
<Group view="presentation" hide-input="false" hide-output="true" inline-output="false" labelreference="L2349" drawlabel="true">
<Input>
<Text-field style="Text" layout="Normal"><Font italic="true">Calendar      </Font>                   <EC-RadioButton id="RadioButton28" groupname="Group5" caption="USD LIBOR" enabled="true" visible="true" selected="true"></EC-RadioButton><EC-RadioButton id="RadioButton29" groupname="Group5" caption="EURIBOR" enabled="true" visible="true" selected="false"></EC-RadioButton><EC-RadioButton id="RadioButton30" groupname="Group5" caption="GBP LIBOR" enabled="true" visible="true" selected="false"></EC-RadioButton><Equation executable="false" style="2D Math" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2I1EhRicvJSxtYXRodmFyaWFudEdRJ25vcm1hbEYn">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=</Equation></Text-field>
</Input>
</Group></Presentation-Block><Presentation-Block>
<Group view="presentation" hide-input="false" hide-output="true" inline-output="false" labelreference="L2407" drawlabel="true">
<Input>
<Text-field style="Text" layout="Normal"><Equation executable="false" style="2D Math" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2I1EhRicvJSxtYXRodmFyaWFudEdRJ25vcm1hbEYn">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=</Equation></Text-field>
</Input>
</Group></Presentation-Block><Presentation-Block>
<Group view="presentation" hide-input="false" hide-output="true" inline-output="false" labelreference="L2424" drawlabel="true">
<Input>
<Text-field style="Text" layout="Normal"><Font italic="true">Payments made every </Font><Equation executable="false" style="2D Math" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbWlHRiQ2I1EhRictSSNtb0dGJDYuUSJ+RicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLyUmZmVuY2VHUSZmYWxzZUYnLyUqc2VwYXJhdG9yR0Y7LyUpc3RyZXRjaHlHRjsvJSpzeW1tZXRyaWNHRjsvJShsYXJnZW9wR0Y7LyUubW92YWJsZWxpbWl0c0dGOy8lJ2FjY2VudEdGOy8lJ2xzcGFjZUdRJjAuMGVtRicvJSdyc3BhY2VHRkpGL0YzRjY=">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbWlHRiQ2I1EhRictSSNtb0dGJDYuUSJ+RicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLyUmZmVuY2VHUSZmYWxzZUYnLyUqc2VwYXJhdG9yR0Y7LyUpc3RyZXRjaHlHRjsvJSpzeW1tZXRyaWNHRjsvJShsYXJnZW9wR0Y7LyUubW92YWJsZWxpbWl0c0dGOy8lJ2FjY2VudEdGOy8lJ2xzcGFjZUdRJjAuMGVtRicvJSdyc3BhY2VHRkpGL0YzRjY=</Equation><EC-MathContainer id="MathContainer13" pixel-width="50" pixel-height="35" expression="&lt;math xmlns='http://www.w3.org/1998/Math/MathML'&gt;&lt;mstyle fontfamily='Times New Roman' mathsize='12pt' mathcolor='#000000'  veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.7099999785423279' scriptminsize='8.0pt'&gt;&lt;mrow&gt;&lt;mn fontweight='normal'&gt;1&lt;/mn&gt;&lt;/mrow&gt;&lt;/mstyle&gt;&lt;/math&gt;" visible="true" show-border="true" autofit="false"></EC-MathContainer><Font italic="true"> months</Font></Text-field>
</Input>
</Group></Presentation-Block><Presentation-Block>
<Group view="presentation" hide-input="false" hide-output="true" inline-output="false" labelreference="L2425" drawlabel="true">
<Input>
<Text-field style="Text" layout="Normal"><Equation executable="false" style="2D Math" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2I1EhRicvJSxtYXRodmFyaWFudEdRJ25vcm1hbEYn">JSFH</Equation></Text-field>
</Input>
</Group></Presentation-Block><Presentation-Block>
<Group view="presentation" hide-input="false" hide-output="true" inline-output="false" labelreference="L2408" drawlabel="true">
<Input>
<Text-field style="Text" layout="Normal"><EC-Button id="Button14" caption="Set" pixel-width="300" pixel-height="200" enabled="true" visible="true" show-border="true" user-size="false"><MapleCode action="click-event-handler">use DocumentTools, Finance in 


Do(a6=DocumentTools[GetProperty]('RadioButton28','value')):
Do(b6=DocumentTools[GetProperty]('RadioButton29','value')):
Do(c6=DocumentTools[GetProperty]('RadioButton30','value')):
Do(c7=%MathContainer13):

if a6=&quot;true&quot; then
	Do(f6=USDLIBOR);
	elif b6=&quot;true&quot; then 
	Do(f6=EURIBOR);
	elif c6=&quot;true&quot; then
	Do(f6=GBPLIBOR);
end if;

Do(benchmark = BenchmarkRate(c7, Months, f6, discount_curve)):
SetProperty(Button8, enabled, &quot;true&quot;):
end use; 
</MapleCode></EC-Button></Text-field>
</Input>
</Group></Presentation-Block></Table-Cell></Table-Row><Table-Row align="top" separator="true"><Table-Cell columnspan="1" backgroundstyle="0" rowspan="1" padding="5" fillcolor="[255,255,255]"><Presentation-Block>
<Group view="presentation" hide-input="false" hide-output="true" inline-output="false" labelreference="L2385" drawlabel="true">
<Input>
<Text-field style="Text" layout="Normal"><Equation executable="false" style="2D Math" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2I1EhRicvJSxtYXRodmFyaWFudEdRJ25vcm1hbEYn">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=</Equation></Text-field>
</Input>
</Group></Presentation-Block></Table-Cell><Table-Cell columnspan="1" backgroundstyle="0" rowspan="1" padding="5" fillcolor="[255,255,255]"><Presentation-Block>
<Group view="presentation" hide-input="false" hide-output="true" inline-output="false" labelreference="L2430" drawlabel="true">
<Input>
<Text-field style="Text" layout="Normal">
<Font italic="true">Nominal Amount of the swap      <EC-MathContainer id="MathContainer14" pixel-width="100" pixel-height="30" expression="&lt;math xmlns='http://www.w3.org/1998/Math/MathML'&gt;&lt;mstyle fontfamily='Times New Roman' mathsize='12pt' mathcolor='#000000'  veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.7099999785423279' scriptminsize='8.0pt'&gt;&lt;mrow&gt;&lt;mn fontweight='normal'&gt;100&lt;/mn&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi mathvariant='normal' fontweight='normal'&gt;&lt;/mi&gt;&lt;/mrow&gt;&lt;/mstyle&gt;&lt;/math&gt;" visible="true" show-border="true" autofit="false"></EC-MathContainer>
Spread over benchmark              <EC-MathContainer id="MathContainer15" pixel-width="100" pixel-height="30" expression="&lt;math xmlns='http://www.w3.org/1998/Math/MathML'&gt;&lt;mstyle fontfamily='Times New Roman' mathsize='12pt' mathcolor='#000000'  veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.7099999785423279' scriptminsize='8.0pt'&gt;&lt;mrow&gt;&lt;mn fontweight='normal'&gt;0.03&lt;/mn&gt;&lt;/mrow&gt;&lt;/mstyle&gt;&lt;/math&gt;" visible="true" show-border="true" autofit="false"></EC-MathContainer></Font></Text-field>
</Input>
</Group></Presentation-Block><Presentation-Block>
<Group view="presentation" hide-input="false" hide-output="true" inline-output="false" labelreference="L2434" drawlabel="true">
<Input>
<Text-field style="Text" layout="Normal"><Font italic="true">Interest rate of the fixed leg        <EC-MathContainer id="MathContainer16" pixel-width="100" pixel-height="30" expression="&lt;math xmlns='http://www.w3.org/1998/Math/MathML'&gt;&lt;mstyle fontfamily='Times New Roman' mathsize='12pt' mathcolor='#000000'  veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.7099999785423279' scriptminsize='8.0pt'&gt;&lt;mrow&gt;&lt;mn fontweight='normal'&gt;0.0&lt;/mn&gt;&lt;/mrow&gt;&lt;/mstyle&gt;&lt;/math&gt;" visible="true" show-border="true" autofit="false"></EC-MathContainer></Font></Text-field>
</Input>
</Group></Presentation-Block><Presentation-Block>
<Group view="presentation" hide-input="false" hide-output="true" inline-output="false" labelreference="L2432" drawlabel="true">
<Input>
<Text-field style="Text" italic="true" layout="Normal" alignment="centred"></Text-field>
</Input>
</Group></Presentation-Block><Presentation-Block>
<Group view="presentation" hide-input="false" hide-output="true" inline-output="false" labelreference="L2386" drawlabel="true">
<Input>
<Text-field style="Text" layout="Normal" alignment="centred"><EC-Button id="Button8" caption="Build the Baseline  Interest Rate Swap" pixel-width="300" pixel-height="200" enabled="true" visible="true" show-border="true" user-size="false"><MapleCode action="click-event-handler">use DocumentTools, Finance in 

Do(nominal=%MathContainer14):
Do(spread=%MathContainer15):
Do(_fixedrate=%MathContainer16):
#Do(swap=InterestRateSwap(nominal, _fixedrate, Sch1, benchmark, Sch2, spread)):
Do(swap=InterestRateSwap(nominal, 0.0, Sch1, benchmark, Sch2, 0.0)):


Do(rate= FairRate(swap, discount_curve)):
Do(%MathContainer17=rate):

Do(cash_flows=CashFlows(swap, paying)):
Do(dates = map(proc (t) options operator, arrow; t[date] end proc, cash_flows));

SetProperty(Button15, enabled, &quot;true&quot;):
SetProperty(Button17, enabled, &quot;true&quot;):
end use; 
</MapleCode></EC-Button><Equation executable="false" style="2D Math" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2I1EhRicvJSxtYXRodmFyaWFudEdRJ25vcm1hbEYn">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=</Equation></Text-field>
</Input>
</Group></Presentation-Block></Table-Cell></Table-Row></Table><Presentation-Block>
<Group view="presentation" hide-input="false" hide-output="true" inline-output="false" labelreference="L9285" drawlabel="true" redirect-target="L9356">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal"><Equation executable="true" style="2D Input" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2I1EhRicvJStleGVjdXRhYmxlR1EmZmFsc2VGJy8lLG1hdGh2YXJpYW50R1Enbm9ybWFsRic=">JSFH</Equation></Text-field>
</Input>
</Group>
<Group view="presentation" hide-input="false" hide-output="true" inline-output="false" labelreference="L9283" drawlabel="true" redirect-target="L9251">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal"></Text-field>
</Input>
</Group>
<Group view="presentation" hide-input="false" hide-output="true" inline-output="false" labelreference="L2306" drawlabel="true" redirect-target="L9251">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal"></Text-field>
</Input>
</Group></Presentation-Block><Table interior="group" showinput="true" alignment="left" exterior="all" width="71.83908045977012%" labelreference="L2526" showlabel="true" captionalignment="0" title="" order="row" drawcaption="false" randomized="false" captionposition="1" plotalignlists="" pagebreak="cell" postexecute="insert" showgroup="true"><Table-Column weight="209" separator="true"></Table-Column><Table-Column weight="541" separator="true"></Table-Column><Table-Row align="top" separator="true"><Table-Cell columnspan="1" backgroundstyle="1" rowspan="1" padding="5" fillcolor="[204,255,255]"><Presentation-Block>
<Group view="presentation" hide-input="false" hide-output="true" inline-output="false" labelreference="L2527" drawlabel="true">
<Input>
<Text-field style="Text" size="14" bold="true" layout="Normal"></Text-field>
</Input>
</Group></Presentation-Block></Table-Cell><Table-Cell columnspan="1" backgroundstyle="1" rowspan="1" padding="5" fillcolor="[204,255,255]"><Presentation-Block>
<Group view="presentation" hide-input="false" hide-output="true" inline-output="false" labelreference="L2528" drawlabel="true">
<Input>
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<Text-field style="Text" layout="Normal"><Font italic="true">(Hull White Model)</Font></Text-field>
</Input>
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<Text-field style="Text" italic="true" layout="Normal" alignment="centred"><Font italic="true">
a <EC-TextArea id="TextArea42" enabled="true" visible="true" visiblecharacterwidth="10" visiblerows="1" contents="0.048696" editable="true" wrapping="true" show-border="true" password="false"></EC-TextArea><Font encoding="UTF-8">   \317\203<EC-TextArea id="TextArea43" enabled="true" visible="true" visiblecharacterwidth="10" visiblerows="1" contents="0.0058904" editable="true" wrapping="true" show-border="true" password="false"></EC-TextArea></Font> </Font></Text-field>
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<Text-field style="Text" italic="true" layout="Normal" alignment="centred"></Text-field>
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<Text-field style="Text" italic="true" layout="Normal" alignment="centred"><Font italic="true">Steps per path <EC-TextArea id="TextArea44" enabled="true" visible="true" visiblecharacterwidth="10" visiblerows="1" contents="19" editable="true" wrapping="true" show-border="true" password="false"></EC-TextArea></Font></Text-field>
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<Text-field style="Text" italic="true" layout="Normal" alignment="centred"><EC-Button id="Button15" caption="Create the Interest Rate Model" pixel-width="300" pixel-height="200" enabled="true" visible="true" show-border="true" user-size="false"><MapleCode action="click-event-handler">use DocumentTools, Finance in 

Do(WH_a=%TextArea42):
Do(WH_sigma=%TextArea43):
Do(model=HullWhiteModel(discount_curve, WH_a, WH_sigma)):
Do(TWH=ShortRateTree(model, 0.90*max(times), %TextArea44)):
Do(%Plot5=TreePlot(TWH, gridlines = true, thickness = 1, axes = BOXED, labels=[&quot;years&quot;, &quot;rates&quot;],
labeldirections=[horizontal,vertical])):
SetProperty(Button18, enabled, &quot;true&quot;):
end use; 
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</Input>
</Group></Presentation-Block></Table-Cell></Table-Row></Table>
<Text-field superscript="false" placeholder="false" executable="false" selection-placeholder="false" italic="false" size="12" bold="false" subscript="false" family="Times New Roman" opaque="false" underline="false" background="[255,255,255]" readonly="false" foreground="[0,0,0]" alignment="left" firstindent="0" spacebelow="0" leftmargin="0" linespacing="0.0" initial="0" linebreak="space" rightmargin="0" bulletsuffix="" spaceabove="0" bullet="none" pagebreak-before="false"></Text-field><Table interior="group" showinput="true" alignment="left" exterior="all" width="47.79693486590038%" labelreference="L9150" showlabel="true" captionalignment="0" title="" order="row" drawcaption="false" randomized="false" captionposition="1" plotalignlists="" pagebreak="cell" postexecute="insert" showgroup="true"><Table-Column weight="499" separator="true"></Table-Column><Table-Row align="top" separator="true"><Table-Cell columnspan="1" backgroundstyle="1" rowspan="1" padding="5" fillcolor="[153,204,255]"><Presentation-Block>
<Group view="presentation" hide-input="false" hide-output="true" inline-output="false" labelreference="L9152" drawlabel="true">
<Input>
<Text-field style="Text" layout="Normal" alignment="centred"><Font bold="true" size="14">Swaption Parametrization and Valuation Module</Font></Text-field>
</Input>
</Group></Presentation-Block></Table-Cell></Table-Row><Table-Row align="top" separator="true"><Table-Cell columnspan="1" backgroundstyle="1" rowspan="1" padding="5" fillcolor="[204,255,255]"><Presentation-Block>
<Group view="presentation" hide-input="false" hide-output="true" inline-output="false" labelreference="L9194" drawlabel="true">
<Input>
<Text-field style="Text" layout="Normal" alignment="centred"><Font bold="true" italic="true">Strike Rate</Font></Text-field>
</Input>
</Group></Presentation-Block></Table-Cell></Table-Row><Table-Row align="top" separator="true"><Table-Cell columnspan="1" backgroundstyle="0" rowspan="1" padding="5" fillcolor="[255,255,255]"><Presentation-Block>
<Group view="presentation" hide-input="false" hide-output="true" inline-output="false" labelreference="L9154" drawlabel="true">
<Input>
<Text-field style="Text" italic="true" layout="Normal" alignment="centred"><Font italic="true">Fair Rate of the Swap  <EC-MathContainer id="MathContainer17" pixel-width="120" pixel-height="25" expression="&lt;math xmlns='http://www.w3.org/1998/Math/MathML'&gt;&lt;mstyle fontfamily='Times New Roman' mathsize='12pt' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'&gt;&lt;mn fontstyle='2D Input' fontweight='normal'&gt;0.04996933011&lt;/mn&gt;&lt;/mstyle&gt;&lt;/math&gt;" visible="true" show-border="true" autofit="false"></EC-MathContainer></Font></Text-field>
</Input>
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<Group view="presentation" hide-input="false" hide-output="true" inline-output="false" labelreference="L9191" drawlabel="true">
<Input>
<Text-field style="Text" italic="true" layout="Normal" alignment="centred"><Font italic="true">K/Fair rate</Font></Text-field>
</Input>
</Group></Presentation-Block><Presentation-Block>
<Group view="presentation" hide-input="false" hide-output="true" inline-output="false" labelreference="L9156" drawlabel="true">
<Input>
<Text-field style="Text" italic="true" layout="Normal" alignment="centred"><EC-Slider id="Slider0" lower-bound="0.4" upper-bound="1.6" control-position="0.86666667" major-tick-spacing="0.4" minor-ticks="0.05" inputenabled="true" visible="true" filled="true" orientation="false" show-labels="true" show-ticks="true" snap-to-ticks="false" continuous-update="false" pixel-width="190" pixel-height="38"></EC-Slider><Font italic="true">      

<EC-Button id="Button17" caption="Fixed Leg Reference for the Swaption" pixel-width="300" pixel-height="200" enabled="true" visible="true" show-border="true" user-size="false"><MapleCode action="click-event-handler">use DocumentTools, Finance in 
Do(_strikerate=rate*%Slider0):
Do(%MathContainer18=_strikerate):
end use; 
</MapleCode></EC-Button><EC-MathContainer id="MathContainer18" pixel-width="120" pixel-height="25" expression="&lt;math xmlns='http://www.w3.org/1998/Math/MathML'&gt;&lt;mstyle fontfamily='Times New Roman' mathsize='12pt' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'&gt;&lt;mn fontstyle='2D Input' fontweight='normal'&gt;0.04330675293&lt;/mn&gt;&lt;/mstyle&gt;&lt;/math&gt;" visible="true" show-border="true" autofit="false"></EC-MathContainer></Font></Text-field>
</Input>
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<Group view="presentation" hide-input="false" hide-output="true" inline-output="false" labelreference="L9184" drawlabel="true">
<Input>
<Text-field style="Text" italic="true" layout="Normal" alignment="centred"><Font bold="true" italic="true">Construction of the Swaption</Font></Text-field>
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Do(nswap=InterestRateSwap(nominal, %MathContainer18, Sch1, benchmark, Sch2, 0.0)):
Do(cash_flows=CashFlows(nswap, paying)):
Do(dates = map(proc (t) options operator, arrow; t[date] end proc, cash_flows));

Do(zz=1*%MathContainer21):
Do(_swaption= EuropeanSwaption(nswap, AdvanceDate(dates[zz], 1, Days, f3)));
Do(%MathContainer22=Finance[LatticePrice](_swaption, TWH, 0.1e-1)):

end use; 
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