daycounter =  a string containing a date specification in a format recognized by ParseDate or a Date data structure -- This option specifies a day counter or day counting convention.

referencedate =  a string containing a date specification in a format recognized by ParseDate or a Date data structure -- This option specifies the reference date, that is, the date when the discount factor is 1. By default this is set to the global evaluation date.

The BlackPrice command computes the price of an interest rate instrument (such as Cap, Floor, Collar or InterestRateSwap) using the Black model with the specified discount rate and volatility.

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

$\mathrm{SetEvaluationDate}\left(''November\; 17,\; 2006''\right)\:$

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

$''November\; 17,\; 2006''$

$\mathrm{nominalamt}≔100$

$\mathrm{nominalamt}≔100$

$\mathrm{benchmark}≔\mathrm{BenchmarkRate}\left(6\,\mathrm{Months}\,\mathrm{EURIBOR}\,0.05\right)$

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

$\mathrm{discount\_curve}≔\mathrm{ForwardCurve}\left(0.05\,'\mathrm{daycounter}'=\mathrm{Actual360}\right)$

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

$\mathrm{start\_date}≔\mathrm{AdvanceDate}\left(2\,\mathrm{Days}\right)$

$\mathrm{start\_date}≔''November\; 19,\; 2006''$

$\mathrm{end\_date}≔\mathrm{AdvanceDate}\left(\mathrm{start\_date}\,20\,\mathrm{Years}\,'\mathrm{convention}'=\mathrm{ModifiedFollowing}\right)$

$\mathrm{end\_date}≔''November\; 19,\; 2026''$

$\mathrm{coupon\_dates}≔\left[\mathrm{seq}\left(\mathrm{AdvanceDate}\left(\mathrm{start\_date}\,6i\,\mathrm{Months}\right)\,i=0..40\right)\right]\:$

$\mathrm{floating\_leg}≔\left[\mathrm{seq}\left(\mathrm{ParCoupon}\left(\mathrm{nominalamt}\,\mathrm{discount\_curve}\,\mathrm{coupon\_dates}\left[i\right]\,\mathrm{coupon\_dates}\left[i+1\right]\right)\,i=1..40\right)\right]\:$

$\mathrm{ir\_cap}≔\mathrm{Cap}\left(\mathrm{floating\_leg}\,0.07\right)$

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

$\mathrm{ir\_floor}≔\mathrm{Floor}\left(\mathrm{floating\_leg}\,0.03\right)$

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

$\mathrm{ir\_collar}≔\mathrm{Collar}\left(\mathrm{floating\_leg}\,0.07\,0.03\right)$

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

$\mathrm{cap\_price}≔\mathrm{BlackPrice}\left(\mathrm{ir\_cap}\,0.05\,0.2\right)$

$\mathrm{cap\_price}≔6.832847321$

$\mathrm{floor\_price}≔\mathrm{BlackPrice}\left(\mathrm{ir\_floor}\,0.05\,0.2\right)$

$\mathrm{floor\_price}≔2.642595692$

$\mathrm{collar\_price}≔\mathrm{BlackPrice}\left(\mathrm{ir\_collar}\,0.05\,0.2\right)$

$\mathrm{collar\_price}≔4.190251628$

$\mathrm{cap\_price}=\mathrm{floor\_price}+\mathrm{collar\_price}$

$6.832847321=6.832847320$

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

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