calculate the yield of a bond given its dirty price - Maple Help

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Finance[YieldFromDirtyPrice] - calculate the yield of a bond given its dirty price

 Calling Sequence YieldFromDirtyPrice(bond, price, compounding, opts)

Parameters

 bond - fixed- or floating-rate bond data structure; bond price - non-negative constant; bond's dirty price compounding - Simple, Continuous, Compounded, or SimpleThenCompounded; the underlying compounding type opts - equations of the form option = value where option is one of accuracy, iterations, or evaluationdate; specify options for the YieldFromDirtyPrice command

Description

 • The YieldFromDirtyPrice command calculates a bond's yield based on the specified dirty price.
 • The parameter bond can be either a fixed-rate bond or a floating-rate bond.
 • The parameter price is the desired dirty price.
 • The (optional) parameter compounding specifies what type of compounding will be used to calculate the yield. By default Continuous compounding is assumed.

Examples

 > $\mathrm{with}\left(\mathrm{Finance}\right):$
 > $\mathrm{SetEvaluationDate}\left("November 25, 2006"\right):$
 > $\mathrm{EvaluationDate}\left(\right)$
 ${"November 25, 2006"}$ (1)
 > $\mathrm{Settings}\left(\left[\mathrm{daycounter}=\mathrm{Historical},\mathrm{settlementdays}=0,\mathrm{businessdayconvention}=\mathrm{Unadjusted},\mathrm{compounding}=\mathrm{Continuous}\right]\right)$
 $\left[{\mathrm{daycounter}}{=}{\mathrm{Historical}}{,}{\mathrm{settlementdays}}{=}{0}{,}{\mathrm{businessdayconvention}}{=}{\mathrm{Unadjusted}}{,}{\mathrm{compounding}}{=}{\mathrm{Continuous}}\right]$ (2)

Consider a zero-coupon bond with a face value of 100 maturing in five years.

 > $\mathrm{bond1}:=\mathrm{ZeroCouponBond}\left(100,5,\mathrm{Years}\right):$
 > $\mathrm{price1}:=\mathrm{DirtyPrice}\left(\mathrm{bond1},0.05,\mathrm{Compounded}\right)$
 ${\mathrm{price1}}{:=}{78.35261665}$ (3)
 > $\mathrm{yield1}:=\mathrm{YieldFromDirtyPrice}\left(\mathrm{bond1},\mathrm{price1}\right)$
 ${\mathrm{yield1}}{:=}{0.04879016417}$ (4)
 > $\mathrm{EquivalentRate}\left(\mathrm{yield1},\mathrm{Continuous},\mathrm{Annual}\right)$
 ${0.05000000000}$ (5)
 > $\mathrm{yield1}:=\mathrm{YieldFromDirtyPrice}\left(\mathrm{bond1},\mathrm{price1},\mathrm{Compounded}\right)$
 ${\mathrm{yield1}}{:=}{0.05000000006}$ (6)

Consider a 3-year bond with a face value of 100 that pays a fixed coupon of 3% issued on March 15, 2005.

 > $\mathrm{Settings}\left(\mathrm{daycounter}=\mathrm{Thirty360European}\right):$
 > $\mathrm{Settings}\left(\mathrm{daycounter}\right)$
 ${\mathrm{Thirty360European}}$ (7)
 > $\mathrm{principal2}:=100:$
 > $\mathrm{coupon2}:=0.03:$
 > $\mathrm{rate2}:=0.05:$
 > $\mathrm{bond2}:=\mathrm{FixedCouponBond}\left(\mathrm{principal2},3,\mathrm{Years},\mathrm{coupon2},\mathrm{issuedate}="March 17, 2005"\right):$

Calculate the bond's dirty price given its yield and vice-versa.

 > $\mathrm{yield2}:=\mathrm{YieldFromDirtyPrice}\left(\mathrm{bond2},100,\mathrm{Compounded}\right)$
 ${\mathrm{yield2}}{:=}{0.04649381416}$ (8)
 > $\mathrm{dirtyprice2}:=\mathrm{DirtyPrice}\left(\mathrm{bond2},\mathrm{yield2},\mathrm{Compounded}\right)$
 ${\mathrm{dirtyprice2}}{:=}{100.0000000}$ (9)
 > $\mathrm{YieldFromDirtyPrice}\left(\mathrm{bond2},\mathrm{dirtyprice2}\right)$
 ${0.04544535191}$ (10)
 > $\mathrm{dirtyprice2}:=\mathrm{DirtyPrice}\left(\mathrm{bond2},\mathrm{rate2}\right)$
 ${\mathrm{dirtyprice2}}{:=}{99.41803696}$ (11)
 > $\mathrm{YieldFromDirtyPrice}\left(\mathrm{bond2},\mathrm{dirtyprice2}\right)$
 ${0.05000000002}$ (12)

Consider the same bond but with semi-annual coupons.

 > $\mathrm{bond3}:=\mathrm{FixedCouponBond}\left(\mathrm{principal2},3,\mathrm{Years},\mathrm{coupon2},\mathrm{issuedate}="March 17, 2005",\mathrm{frequency}=\mathrm{Semiannual}\right):$

Calculate the bond's dirty price given its yield and vice-versa.

 > $\mathrm{yield3}:=\mathrm{YieldFromDirtyPrice}\left(\mathrm{bond3},100,\mathrm{Compounded}\right)$
 ${\mathrm{yield3}}{:=}{0.03443376844}$ (13)
 > $\mathrm{dirtyprice3}:=\mathrm{DirtyPrice}\left(\mathrm{bond3},\mathrm{yield3},\mathrm{Compounded}\right)$
 ${\mathrm{dirtyprice3}}{:=}{100.0000000}$ (14)
 > $\mathrm{YieldFromDirtyPrice}\left(\mathrm{bond3},\mathrm{dirtyprice3}\right)$
 ${0.03414070640}$ (15)
 > $\mathrm{dirtyprice3}:=\mathrm{DirtyPrice}\left(\mathrm{bond3},\mathrm{rate2}\right)$
 ${\mathrm{dirtyprice3}}{:=}{97.97675295}$ (16)
 > $\mathrm{YieldFromDirtyPrice}\left(\mathrm{bond3},\mathrm{dirtyprice3}\right)$
 ${0.05000000002}$ (17)

Note that since the bond has semi-annual coupons, the Compounded yield is based on semi-annual compounding.

 > $\mathrm{dirtyprice3}:=\mathrm{DirtyPrice}\left(\mathrm{bond3},\mathrm{rate2},\mathrm{Compounded}\right)$
 ${\mathrm{dirtyprice3}}{:=}{98.05440635}$ (18)
 > $\mathrm{cashflows3}:=\mathrm{CashFlows}\left(\mathrm{bond3}\right)$
 ${\mathrm{cashflows3}}{:=}\left[{\mathrm{1.500000000 on \text{'}March 17, 2007\text{'}}}{,}{\mathrm{1.500000000 on \text{'}September 17, 2007\text{'}}}{,}{\mathrm{1.500000000 on \text{'}March 17, 2008\text{'}}}{,}{\mathrm{100. on \text{'}March 17, 2008\text{'}}}\right]$ (19)
 > $\mathrm{add}\left({t}_{\mathrm{amount}}\mathrm{DiscountFactor}\left(\mathrm{rate2},{t}_{\mathrm{date}},\mathrm{compounding}=\mathrm{Semiannual}\right),t\phantom{\rule[-0.0ex]{0.5em}{0.0ex}}∈\phantom{\rule[-0.0ex]{0.5em}{0.0ex}}\mathrm{cashflows3}\right)$
 ${98.05440635}$ (20)

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