Financial Engineering: New Applications
http://www.maplesoft.com/applications/category.aspx?cid=219
en-us2014 Maplesoft, A Division of Waterloo Maple Inc.Maplesoft Document SystemFri, 18 Apr 2014 18:08:55 GMTFri, 18 Apr 2014 18:08:55 GMTNew applications in the Financial Engineering categoryhttp://www.mapleprimes.com/images/mapleapps.gifFinancial Engineering: New Applications
http://www.maplesoft.com/applications/category.aspx?cid=219
Downloading Stock Prices and Plotting Returns Distributions
http://www.maplesoft.com/applications/view.aspx?SID=153539&ref=Feed
<p>This application:</p>
<ul>
<li>downloads historical stock prices from Yahoo Finance,</li>
<li>calculates the returns,</li>
<li>plots the distribution of the returns in a histogram,</li>
<li>and overlays a normal distribution with the same mean and standard deviation as the historical data.</li>
<li>The application uses Maple 18's improved Internet connectivity; you can now download data from a URL straight into a matrix using <span ><a href="http://www.maplesoft.com/support/help/Maple/view.aspx?path=ImportMatrix">ImportMatrix()</a></span>.</li>
</ul><img src="/view.aspx?si=153539/stockreturns.png" alt="Downloading Stock Prices and Plotting Returns Distributions" align="left"/><p>This application:</p>
<ul>
<li>downloads historical stock prices from Yahoo Finance,</li>
<li>calculates the returns,</li>
<li>plots the distribution of the returns in a histogram,</li>
<li>and overlays a normal distribution with the same mean and standard deviation as the historical data.</li>
<li>The application uses Maple 18's improved Internet connectivity; you can now download data from a URL straight into a matrix using <span ><a href="http://www.maplesoft.com/support/help/Maple/view.aspx?path=ImportMatrix">ImportMatrix()</a></span>.</li>
</ul>153539Thu, 03 Apr 2014 04:00:00 ZSamir KhanSamir KhanThe Greeks
http://www.maplesoft.com/applications/view.aspx?SID=153533&ref=Feed
<p>In mathematical finance, The Greeks are measurements of risk that are used to represent the sensitivity of the price of a derivative to underlying variables, such as time-value decay and the implied volatility or price of the underlying asset.<br /><br /></p>
<p>This application calculates the Greeks for a European call or put option using the Black-Scholes model.</p><img src="/view.aspx?si=153533/TheGreeks.png" alt="The Greeks" align="left"/><p>In mathematical finance, The Greeks are measurements of risk that are used to represent the sensitivity of the price of a derivative to underlying variables, such as time-value decay and the implied volatility or price of the underlying asset.<br /><br /></p>
<p>This application calculates the Greeks for a European call or put option using the Black-Scholes model.</p>153533Mon, 24 Mar 2014 04:00:00 ZMaplesoftMaplesoftJump-diffusion stochastic processes with Maple
http://www.maplesoft.com/applications/view.aspx?SID=153516&ref=Feed
<p>The application presents and definition, creation and handling of jump-diffusion processes. In general, jump-diffusion is an extension to the theory of stochastic processes where the underlying parameters exhibit shocks and "jump" to their new values. Stochasticity with jumps is well recognised in several scientific branches including physics, chemistry, biology, but also economic and finance. The application looks at the example of the last-mentioned fields where the theory of jump-diffusions has been particularly actively researched and applied.</p><img src="/view.aspx?si=153516/Jump_image1.jpg" alt="Jump-diffusion stochastic processes with Maple" align="left"/><p>The application presents and definition, creation and handling of jump-diffusion processes. In general, jump-diffusion is an extension to the theory of stochastic processes where the underlying parameters exhibit shocks and "jump" to their new values. Stochasticity with jumps is well recognised in several scientific branches including physics, chemistry, biology, but also economic and finance. The application looks at the example of the last-mentioned fields where the theory of jump-diffusions has been particularly actively researched and applied.</p>153516Sat, 08 Mar 2014 05:00:00 ZIgor HlivkaIgor HlivkaCar Loan Calculator
http://www.maplesoft.com/applications/view.aspx?SID=145174&ref=Feed
<p>This loan calculator facilitates the life of a borrower. By entering the <strong>purchase price</strong>, the <strong>down payment</strong>, the <strong>number of years</strong> it takes to repay the loan, the <strong>payment frequency</strong>, the <strong>annual interest rate</strong>, and clicking on the "<strong>calculate</strong>" buttom, the calculator will give you the <strong>amount of payment</strong> for each payment period.</p>
<p> </p>
<p>Want to make a loan? Try it out and see how things change with respect to each element.</p><img src="/applications/images/app_image_blank_lg.jpg" alt="Car Loan Calculator" align="left"/><p>This loan calculator facilitates the life of a borrower. By entering the <strong>purchase price</strong>, the <strong>down payment</strong>, the <strong>number of years</strong> it takes to repay the loan, the <strong>payment frequency</strong>, the <strong>annual interest rate</strong>, and clicking on the "<strong>calculate</strong>" buttom, the calculator will give you the <strong>amount of payment</strong> for each payment period.</p>
<p> </p>
<p>Want to make a loan? Try it out and see how things change with respect to each element.</p>145174Wed, 27 Mar 2013 04:00:00 ZZinan WangZinan WangPricing European Call Options with FFTs
http://www.maplesoft.com/applications/view.aspx?SID=144589&ref=Feed
<p>This application compares the price of a European call option with FFTs (using the approach outlined by Carr & Madan in <em>Option Pricing Using the Fast Fourier Transform</em>) and the analytical approach. The application uses the efficient FFT function offered by Maple 17’s new <a href="/products/maple/new_features/signal_processing.aspx">Signal Processing tools</a>.</p><img src="/applications/images/app_image_blank_lg.jpg" alt="Pricing European Call Options with FFTs" align="left"/><p>This application compares the price of a European call option with FFTs (using the approach outlined by Carr & Madan in <em>Option Pricing Using the Fast Fourier Transform</em>) and the analytical approach. The application uses the efficient FFT function offered by Maple 17’s new <a href="/products/maple/new_features/signal_processing.aspx">Signal Processing tools</a>.</p>144589Wed, 13 Mar 2013 04:00:00 ZSamir KhanSamir KhanPortfolio Optimization with the Omega Ratio
http://www.maplesoft.com/applications/view.aspx?SID=140702&ref=Feed
<P>This application finds the asset weights that maximize the Omega Ratio of a portfolio of ten investments, given their simulated monthly returns and a target return. This is a non-convex problem, and requires global optimizers for a rigorous solution. However, a transformation of the variables (only valid for Omega Ratios of over 1) converts the optimization into a linear program.<P>This application implements both approaches, the former using Maple's <A HREF="/products/toolboxes/globaloptimization/">Global Optimization Toolbox</A>, and the latter using Maple's <A HREF="/support/help/AddOns/view.aspx?path=Tour/opt1">linear programming</A> features. For the data set provided in this application, both approaches give comparable results.<img src="/view.aspx?si=140702/140702_thumb.jpg" alt="Portfolio Optimization with the Omega Ratio" align="left"/><P>This application finds the asset weights that maximize the Omega Ratio of a portfolio of ten investments, given their simulated monthly returns and a target return. This is a non-convex problem, and requires global optimizers for a rigorous solution. However, a transformation of the variables (only valid for Omega Ratios of over 1) converts the optimization into a linear program.<P>This application implements both approaches, the former using Maple's <A HREF="/products/toolboxes/globaloptimization/">Global Optimization Toolbox</A>, and the latter using Maple's <A HREF="/support/help/AddOns/view.aspx?path=Tour/opt1">linear programming</A> features. For the data set provided in this application, both approaches give comparable results.140702Thu, 22 Nov 2012 05:00:00 ZSamir KhanSamir KhanGreat Expectations
http://www.maplesoft.com/applications/view.aspx?SID=127116&ref=Feed
<p>An investor is offered what appears to be a great investment opportunity. Unfortunately it doesn't turn out to be so great in the long run. This interactive Maple document explores the situation using simulation and analysis, and suggests a new strategy that would produce better results.</p>
<p>This is an example suitable for presentation in an undergraduate course on probability. No knowledge of Maple is required.</p><img src="/view.aspx?si=127116/expectation_thum.png" alt="Great Expectations" align="left"/><p>An investor is offered what appears to be a great investment opportunity. Unfortunately it doesn't turn out to be so great in the long run. This interactive Maple document explores the situation using simulation and analysis, and suggests a new strategy that would produce better results.</p>
<p>This is an example suitable for presentation in an undergraduate course on probability. No knowledge of Maple is required.</p>127116Thu, 27 Oct 2011 04:00:00 ZAn Interactive Stock Quote Importer
http://www.maplesoft.com/applications/view.aspx?SID=103805&ref=Feed
Financial engineers and quantitative analysts often exploit network services to retrieve stock quotes. A large number of services exist, including paid-for real-time feeds from Bloomberg and Reuters. Yahoo, however, provide a free service that is delayed by fifteen minutes.
The Interactive Stock Quote Importer in this worksheet will import quotes (including historical data) from Yahoo for a series of user-specified NYSE stock symbols. This application
provides text fields for specifying up to five ticker symbols,
allows the user to pick those quantities they want to import with check boxes,
summarises the data in a table,
assigns the values to variables for further processing and analysis.<img src="/view.aspx?si=103805/thumb.jpg" alt="An Interactive Stock Quote Importer" align="left"/>Financial engineers and quantitative analysts often exploit network services to retrieve stock quotes. A large number of services exist, including paid-for real-time feeds from Bloomberg and Reuters. Yahoo, however, provide a free service that is delayed by fifteen minutes.
The Interactive Stock Quote Importer in this worksheet will import quotes (including historical data) from Yahoo for a series of user-specified NYSE stock symbols. This application
provides text fields for specifying up to five ticker symbols,
allows the user to pick those quantities they want to import with check boxes,
summarises the data in a table,
assigns the values to variables for further processing and analysis.103805Wed, 06 Apr 2011 04:00:00 ZMaplesoftMaplesoftFinancial Modeling in Maple
http://www.maplesoft.com/applications/view.aspx?SID=103793&ref=Feed
The Finance package is new in Maple 15. It contains many tools for advanced financial modeling, as well as accessible tools for personal finance. On the personal finance side, there are tools that can be used for computing with mortgages or retirement packages. The financial modeling tools include a wide range of stochastic processes that can be used to model option prices, such as Brownian motion, Ito processes, an SVJJ process, and more. It also includes tools to compose complex processes out of these building blocks. You can also create, manipulate, and analyze many types of financial instruments, such as American, Bermudan, and European options and swaptions and several types of bonds; short rate models; term structures of interest rates; and cash flows. The instruments can then be priced using analytic methods, lattice methods or Monte Carlo simulation - all using one of many date arithmetic conventions. Finally, the processes occurring in the package can be visualized in several ways.<img src="/view.aspx?si=103793/thumb.jpg" alt="Financial Modeling in Maple" align="left"/>The Finance package is new in Maple 15. It contains many tools for advanced financial modeling, as well as accessible tools for personal finance. On the personal finance side, there are tools that can be used for computing with mortgages or retirement packages. The financial modeling tools include a wide range of stochastic processes that can be used to model option prices, such as Brownian motion, Ito processes, an SVJJ process, and more. It also includes tools to compose complex processes out of these building blocks. You can also create, manipulate, and analyze many types of financial instruments, such as American, Bermudan, and European options and swaptions and several types of bonds; short rate models; term structures of interest rates; and cash flows. The instruments can then be priced using analytic methods, lattice methods or Monte Carlo simulation - all using one of many date arithmetic conventions. Finally, the processes occurring in the package can be visualized in several ways.103793Wed, 06 Apr 2011 04:00:00 ZMaplesoftMaplesoftCopula function in multivariate dependency analysis
http://www.maplesoft.com/applications/view.aspx?SID=100528&ref=Feed
<p>Copula is a constructor function for multivariate distribution from univariate marginals. It is a method to link univariate samples, not necessarily from identical distributions, into joint multivariate distributions. In this way, copulas are more generic and flexible functions to study dependency arising from multivariate distributions.</p>
<p>Conceptually, copulas are based on transformation of the underlying marginal into new derived variable with uniform distribution. Consequently, any multivariate distribution can be expressed in the form of copula function. If each marginal is continuous then copula is unique. Sklar in 1959 was the first to point this out.</p>
<p>Copulas represent a broad set of functions and they generally differ by (i) number of dependency factors and (ii) construction complexity. The choose of copula depends on the nature of the multivariate study and fitting objectives to an underlying data.</p><img src="/view.aspx?si=100528/maple_icon.jpg" alt="Copula function in multivariate dependency analysis" align="left"/><p>Copula is a constructor function for multivariate distribution from univariate marginals. It is a method to link univariate samples, not necessarily from identical distributions, into joint multivariate distributions. In this way, copulas are more generic and flexible functions to study dependency arising from multivariate distributions.</p>
<p>Conceptually, copulas are based on transformation of the underlying marginal into new derived variable with uniform distribution. Consequently, any multivariate distribution can be expressed in the form of copula function. If each marginal is continuous then copula is unique. Sklar in 1959 was the first to point this out.</p>
<p>Copulas represent a broad set of functions and they generally differ by (i) number of dependency factors and (ii) construction complexity. The choose of copula depends on the nature of the multivariate study and fitting objectives to an underlying data.</p>100528Wed, 29 Dec 2010 05:00:00 ZI. HlivkaI. HlivkaGeneration of correlated random numbers
http://www.maplesoft.com/applications/view.aspx?SID=99806&ref=Feed
<p>This application is an extension of an earlier document on multivariate distributions and demonstrates how Maple can be used to generate random samples from such distribution. In a narrow sense, it presents the tool for generation of correlated samples. The sampling need for multi-factor random variables (RV) with a given correlation structure arises in many applications in economics, finance, but also in natural sciences such as genetics, physics etc. and here we show that such task can be accomplished with ease using Maple’s <em>Statistic</em>s and <em>Linear Algebra</em> packages.</p><img src="/view.aspx?si=99806/maple_icon.jpg" alt="Generation of correlated random numbers" align="left"/><p>This application is an extension of an earlier document on multivariate distributions and demonstrates how Maple can be used to generate random samples from such distribution. In a narrow sense, it presents the tool for generation of correlated samples. The sampling need for multi-factor random variables (RV) with a given correlation structure arises in many applications in economics, finance, but also in natural sciences such as genetics, physics etc. and here we show that such task can be accomplished with ease using Maple’s <em>Statistic</em>s and <em>Linear Algebra</em> packages.</p>99806Fri, 03 Dec 2010 05:00:00 ZI. HlivkaI. HlivkaMaple for Commodity Finance
http://www.maplesoft.com/applications/view.aspx?SID=35126&ref=Feed
<p>In this application we show how Maple can handle financial options models that have become popular in commodity finance. The financial trading of commodities has dramatically increased over past years as finance community started to look for non-standard instruments uncorrelated with the traditional financial products such as stocks, bonds, rates and currencies. Commodities, unlike their financial counterparts, require different approach to the process modeling: (i) commodities exhibit seasonality effects, (ii) commodity futures are exposed to many deformation modes, (iii) futures volatility is driven by the "Samuelson" effect that causes its drop as the expiry time shortens.</p><img src="/view.aspx?si=35126/thumb.jpg" alt="Maple for Commodity Finance" align="left"/><p>In this application we show how Maple can handle financial options models that have become popular in commodity finance. The financial trading of commodities has dramatically increased over past years as finance community started to look for non-standard instruments uncorrelated with the traditional financial products such as stocks, bonds, rates and currencies. Commodities, unlike their financial counterparts, require different approach to the process modeling: (i) commodities exhibit seasonality effects, (ii) commodity futures are exposed to many deformation modes, (iii) futures volatility is driven by the "Samuelson" effect that causes its drop as the expiry time shortens.</p>35126Mon, 01 Feb 2010 05:00:00 ZI. HlivkaI. HlivkaOptimal Portfolio Allocation and Economic Utility
http://www.maplesoft.com/applications/view.aspx?SID=4860&ref=Feed
<p>Show how the risk and reward set of a portfolio of two or three securities whose returns are jointly normally distributed is calculated from standard theorems about the mean and variance of linear combinations of the random variables. Use ideas from multivariable calculus to show how the feasible set is derived. Visualize the efficient frontier of the risk and reward set. Visualize the economic utility of the portfolio. Show how the concept of economic utility selects a unique optimal portfolio on the efficient frontier.</p><img src="/view.aspx?si=4860/thumb2.jpg" alt="Optimal Portfolio Allocation and Economic Utility" align="left"/><p>Show how the risk and reward set of a portfolio of two or three securities whose returns are jointly normally distributed is calculated from standard theorems about the mean and variance of linear combinations of the random variables. Use ideas from multivariable calculus to show how the feasible set is derived. Visualize the efficient frontier of the risk and reward set. Visualize the economic utility of the portfolio. Show how the concept of economic utility selects a unique optimal portfolio on the efficient frontier.</p>4860Mon, 14 Sep 2009 04:00:00 ZShengjie GuoShengjie GuoOptions with Foreign Exchange Adjustment
http://www.maplesoft.com/applications/view.aspx?SID=6874&ref=Feed
The document presents the methods used by market practitioners to adjust the financial instruments processes and options valuations when payoffs are converted into different currency. Foreign exchange adjustment in the financial options universe brings in additional stochastic factor that extends the traditional univariate space into bi-variate or even multi-variate setting. We show that key tool to handle this scenario is an appropriate change of probability measure. In this context we also discuss the essence of the Siegel Paradox and show the way to resolve it.<img src="/view.aspx?si=6874/Quanto Options_95.gif" alt="Options with Foreign Exchange Adjustment" align="left"/>The document presents the methods used by market practitioners to adjust the financial instruments processes and options valuations when payoffs are converted into different currency. Foreign exchange adjustment in the financial options universe brings in additional stochastic factor that extends the traditional univariate space into bi-variate or even multi-variate setting. We show that key tool to handle this scenario is an appropriate change of probability measure. In this context we also discuss the essence of the Siegel Paradox and show the way to resolve it.6874Mon, 10 Nov 2008 00:00:00 ZIgor HlivkaIgor HlivkaAsian Options: Analytical Approach
http://www.maplesoft.com/applications/view.aspx?SID=6875&ref=Feed
Asian options are special case of standard financial options where the option's payoff depends on an average value of an underlying asset over the contract's life. The rationale for Asian options comes from various motivations - contrary to the standard option contract, the user may want / need an exposure to an average value of the underlying asset over the whole life of the contract rather than its terminal value.<img src="/view.aspx?si=6875/thumb.jpg" alt="Asian Options: Analytical Approach" align="left"/>Asian options are special case of standard financial options where the option's payoff depends on an average value of an underlying asset over the contract's life. The rationale for Asian options comes from various motivations - contrary to the standard option contract, the user may want / need an exposure to an average value of the underlying asset over the whole life of the contract rather than its terminal value.6875Mon, 10 Nov 2008 00:00:00 ZIgor HlivkaIgor HlivkaPerpetual Options
http://www.maplesoft.com/applications/view.aspx?SID=6688&ref=Feed
Standard financial options are always expressed in terms of pre-determined maturity. Option's contract life can be as short as few days and can run up to several years. On the other hand, perpetual options, as the name suggests, have no fixed maturity and no exercise limits. This makes perpetual options an interesting class of non-standard financial contracts that is worth examining from both theoretical and practical perspectives.<img src="/view.aspx?si=6688/1.jpg" alt="Perpetual Options" align="left"/>Standard financial options are always expressed in terms of pre-determined maturity. Option's contract life can be as short as few days and can run up to several years. On the other hand, perpetual options, as the name suggests, have no fixed maturity and no exercise limits. This makes perpetual options an interesting class of non-standard financial contracts that is worth examining from both theoretical and practical perspectives.6688Tue, 23 Sep 2008 00:00:00 ZIgor HlivkaIgor HlivkaExchange, Basket and Other Multi-Asset Options
http://www.maplesoft.com/applications/view.aspx?SID=6687&ref=Feed
This application demonstration reviews several classes of multi-asset options and as such extends the concept on multi-variability in Finance presented / discussed in other applications. Multi-variability is important concept in financial engineering as many non-standard structured products in the market are exposed to multiple source of randomness. Multi-variability is not trivial in terms of handling multiple dependencies, however suitable change of martingale measure and dimension-reduction techniques can help simplifying the multi-variable process into more manageable routines.
Although multi-dependency in many instances requires numerical processing, we will show that with Maple we can do better. Our aim is to devise an analytical solution to this problem and will show how Maple's symbolic engine can efficiently cope with this task.<img src="/view.aspx?si=6687/thumb2.jpg" alt="Exchange, Basket and Other Multi-Asset Options" align="left"/>This application demonstration reviews several classes of multi-asset options and as such extends the concept on multi-variability in Finance presented / discussed in other applications. Multi-variability is important concept in financial engineering as many non-standard structured products in the market are exposed to multiple source of randomness. Multi-variability is not trivial in terms of handling multiple dependencies, however suitable change of martingale measure and dimension-reduction techniques can help simplifying the multi-variable process into more manageable routines.
Although multi-dependency in many instances requires numerical processing, we will show that with Maple we can do better. Our aim is to devise an analytical solution to this problem and will show how Maple's symbolic engine can efficiently cope with this task.6687Tue, 23 Sep 2008 00:00:00 ZIgor HlivkaIgor HlivkaAn Interactive Stock Quote Importer
http://www.maplesoft.com/applications/view.aspx?SID=6650&ref=Feed
<p>The Interactive Stock Quote Importer in this worksheet will import quotes (including historical data) from Yahoo for a series of user-specified NYSE stock symbols. This application provides text fields for specifying up to five ticker symbols, allows the user to pick those quantities they want to import with check boxes, summarises the data in a table, and assigns the values to variables for further processing and analysis.</p><img src="/view.aspx?si=6650/thumb.gif" alt="An Interactive Stock Quote Importer" align="left"/><p>The Interactive Stock Quote Importer in this worksheet will import quotes (including historical data) from Yahoo for a series of user-specified NYSE stock symbols. This application provides text fields for specifying up to five ticker symbols, allows the user to pick those quantities they want to import with check boxes, summarises the data in a table, and assigns the values to variables for further processing and analysis.</p>6650Thu, 11 Sep 2008 04:00:00 ZMaplesoftMaplesoftMultivariate Distributions In Maple
http://www.maplesoft.com/applications/view.aspx?SID=6352&ref=Feed
The document demonstrates the extension of Maple's comprehensive Statistical package into multivariate setting. It shows how Maple's symbolic analytics and numerical engines can be seamlessly applied in the field of multivariate statistics. The core concept of multivariate analysis - joint distributions - are discussed in the context of multivariate Normal distribution and particular aspects of "jointness" are presented through marginal and conditional densities. Extension of multinormality into related family of joint distributions is shown on the example of multivariate Student-t distribution.<img src="/view.aspx?si=6352/thumb2.jpg" alt="Multivariate Distributions In Maple" align="left"/>The document demonstrates the extension of Maple's comprehensive Statistical package into multivariate setting. It shows how Maple's symbolic analytics and numerical engines can be seamlessly applied in the field of multivariate statistics. The core concept of multivariate analysis - joint distributions - are discussed in the context of multivariate Normal distribution and particular aspects of "jointness" are presented through marginal and conditional densities. Extension of multinormality into related family of joint distributions is shown on the example of multivariate Student-t distribution.6352Tue, 17 Jun 2008 00:00:00 ZIgor HlivkaIgor HlivkaBlack-Scholes Model
http://www.maplesoft.com/applications/view.aspx?SID=1464&ref=Feed
In this application example, we want to compute the option price using three different methods. The first method is to derive the analytical solution to the option price based on the classical Black-Scholes model. Next, we compute the option price through Monte Carlo simulation based on the Black-Scholes model for stock price estimation. Finally, we use the Black-Scholes differential equation model to estimate the option price.<img src="/view.aspx?si=1464/thumb.jpg" alt="Black-Scholes Model" align="left"/>In this application example, we want to compute the option price using three different methods. The first method is to derive the analytical solution to the option price based on the classical Black-Scholes model. Next, we compute the option price through Monte Carlo simulation based on the Black-Scholes model for stock price estimation. Finally, we use the Black-Scholes differential equation model to estimate the option price.1464Tue, 06 May 2008 00:00:00 ZMaplesoftMaplesoft