evaluationdate = a string containing a date specification in a format recognized by ParseDate or a Date data structure -- This option specifies the evaluation date. By default this is set to the global evaluation date (see EvaluationDate).

The DirtyPrice command computes the dirty price of a bond, given its yield. Dirty price does include any accrued interest that has accumulated since the last coupon payment. The dirty price of a bond is the same as the net present value of a bond (see NetPresentValue). See the CleanPrice command to calculate the clean price of a bond, which does not include any accrued interest.

The parameter bond is either a fixed coupon bond or floating rate bond. The parameter yield is the desired yield.

$\mathrm{with}\left(\mathrm{Finance}\right)\:$

$\mathrm{SetEvaluationDate}\left(''November\; 25,\; 2006''\right)\:$

$\mathrm{EvaluationDate}\left(\right)$

$''November\; 25,\; 2006''$

$\mathrm{Settings}\left(\left[\mathrm{daycounter}=\mathrm{Historical}\,\mathrm{settlementdays}=0\,\mathrm{businessdayconvention}=\mathrm{Unadjusted}\right]\right)$

$\left[\mathrm{daycounter}=\mathrm{Historical}\,\mathrm{settlementdays}=0\,\mathrm{businessdayconvention}=\mathrm{Unadjusted}\right]$

$\mathrm{bond1}≔\mathrm{ZeroCouponBond}\left(100\,5\,\mathrm{Years}\right)\:$

$\mathrm{price1}≔\mathrm{DirtyPrice}\left(\mathrm{bond1}\,0.05\,\mathrm{Compounded}\right)$

$\mathrm{price1}≔78.35261665$

$\mathrm{yield1}≔\mathrm{YieldFromDirtyPrice}\left(\mathrm{bond1}\,\mathrm{price1}\right)$

$\mathrm{yield1}≔0.04879016417$

$\mathrm{EquivalentRate}\left(\mathrm{yield1}\,\mathrm{Continuous}\,\mathrm{Annual}\right)$

$0.05000000000$

$\mathrm{yield1}≔\mathrm{YieldFromDirtyPrice}\left(\mathrm{bond1}\,\mathrm{price1}\,\mathrm{Compounded}\right)$

$\mathrm{yield1}≔0.05000000006$

$\mathrm{price1}≔\mathrm{DirtyPrice}\left(\mathrm{bond1}\,0.05\right)$

$\mathrm{price1}≔77.88007831$

$\mathrm{price1}≔\mathrm{NetPresentValue}\left(\mathrm{bond1}\,0.05\right)$

$\mathrm{price1}≔77.88007831$

$\mathrm{InternalRateOfReturn}\left(\mathrm{bond1}\,\mathrm{price1}\right)$

$0.04999999999$

$\mathrm{YieldFromDirtyPrice}\left(\mathrm{bond1}\,\mathrm{price1}\right)$

$0.05000000001$

$\mathrm{principal2}≔100\:$

$\mathrm{coupon2}≔0.03\:$

$\mathrm{rate2}≔0.05\:$

$\mathrm{Settings}\left(\mathrm{daycounter}=\mathrm{Thirty360European}\right)\:$

$\mathrm{Settings}\left(\mathrm{daycounter}\right)$

$\mathrm{Thirty360European}$

$\mathrm{bond2}≔\mathrm{FixedCouponBond}\left(\mathrm{principal2}\,3\,\mathrm{Years}\,\mathrm{coupon2}\,\mathrm{issuedate}=''March\; 15,\; 2005''\right)\:$

$\mathrm{DirtyPrice}\left(\mathrm{bond2}\,\mathrm{rate2}\right)$

$99.44565692$

$\mathrm{discount2}≔\mathrm{ForwardCurve}\left(\mathrm{rate2}\right)\:$

$\mathrm{NetPresentValue}\left(\mathrm{bond2}\,\mathrm{discount2}\right)$

$99.44565692$

$\mathrm{cashflows2}≔\mathrm{CashFlows}\left(\mathrm{bond2}\right)$

$\mathrm{cashflows2}≔\left[\mathrm{3.\; on\; \text{'}March\; 15,\; 2007\text{'}}\,\mathrm{3.\; on\; \text{'}March\; 15,\; 2008\text{'}}\,\mathrm{100.\; on\; \text{'}March\; 15,\; 2008\text{'}}\right]$

$\mathrm{NetPresentValue}\left(\mathrm{cashflows2}\,\mathrm{discount2}\right)$

$99.44565692$

$3\mathrm{DiscountFactor}\left(\mathrm{discount2}\,''March\; 15,\; 2007''\right)+103\mathrm{DiscountFactor}\left(\mathrm{discount2}\,''March\; 15,\; 2008''\right)$

$99.44565692$

$3\exp \left(-0.05\mathrm{YearFraction}\left(''March\; 15,\; 2007''\right)\right)+103\exp \left(-0.05\mathrm{YearFraction}\left(''March\; 15,\; 2008''\right)\right)$

$99.44565692$

$\mathrm{bond3}≔\mathrm{FixedCouponBond}\left(\mathrm{principal2}\,3\,\mathrm{Years}\,\mathrm{coupon2}\,\mathrm{issuedate}=''March\; 15,\; 2005''\,\mathrm{convention}=\mathrm{Following}\,\mathrm{daycounter}=\mathrm{Historical}\right)\:$

$\mathrm{discount3}≔\mathrm{ForwardCurve}\left(\mathrm{rate2}\,\mathrm{daycounter}=\mathrm{Historical}\right)\:$

$\mathrm{NetPresentValue}\left(\mathrm{bond3}\,\mathrm{discount3}\right)$

$99.46206804$

$\mathrm{discount4}≔\mathrm{ForwardCurve}\left(\mathrm{rate2}\,\mathrm{daycounter}=\mathrm{Historical}\,\mathrm{referencedate}=\mathrm{AdjustDate}\left(\mathrm{EvaluationDate}\left(\right)\,\mathrm{convention}=\mathrm{Following}\right)\right)$

$\mathrm{discount4}≔\mathbf{module}\left(\right)\mathbf{end\; module}$

$\mathrm{DirtyPrice}\left(\mathrm{bond3}\,\mathrm{rate2}\,\mathrm{evaluationdate}=\mathrm{AdjustDate}\left(\mathrm{EvaluationDate}\left(\right)\,\mathrm{convention}=\mathrm{Following}\right)\right)$

$99.46206804$

$\mathrm{cashflows3}≔\mathrm{CashFlows}\left(\mathrm{bond3}\right)$

$\mathrm{cashflows3}≔\left[\mathrm{3.\; on\; \text{'}March\; 15,\; 2007\text{'}}\,\mathrm{3.006557377\; on\; \text{'}March\; 15,\; 2008\text{'}}\,\mathrm{100.\; on\; \text{'}March\; 15,\; 2008\text{'}}\right]$

$\mathrm{NetPresentValue}\left(\mathrm{cashflows3}\,\mathrm{discount4}\right)$

$99.46206804$

$\mathrm{add}\left(t\left[\mathrm{amount}\right]\mathrm{DiscountFactor}\left(\mathrm{discount4}\,t\left[\mathrm{date}\right]\right)\,t\mathbf{in}\mathrm{cashflows3}\right)$

$99.46206804$

The Finance[DirtyPrice] command was introduced in Maple 15.

For more information on Maple 15 changes, see Updates in Maple 15.