compounding = Simple, Continuous, Annual, Semiannual, EveryFourthMonth, Quarterly, Bimonthly, Monthly, SimpleThenAnnual, SimpleThenSemiannual, SimpleThenEveryFourthMonth, SimpleThenQuarterly, SimpleThenBimonthly, or SimpleThenMonthly -- This option specifies the compounding type for the returned rate. The default value is Continuous.

The ForwardRate(termstructure, expirytime, maturitytime) and ForwardRate(termstructure, expirytime, maturitytime) calling sequences return the forward interest rate for the specified expiry and maturity. The parameter termstructure can be a zero curve, a discount curve, or a forward curve. The compounding type for the returned rate can be controlled through the corresponding option.

The ForwardRate(termstructure, maturitytime) and ForwardRate(termstructure, maturitytime) calling sequences calculate an approximation of the instantaneous forward interest rate for the maturity maturitytime or maturitydate based on the specified term structure.

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

$\mathrm{times}≔\left[0\,0.5\,1\,1.5\,2\right]\:$

$\mathrm{rates}≔\left[0.03\,0.04\,0.06\,0.07\,0.075\right]\:$

$R≔\mathrm{ZeroCurve}\left(\mathrm{times}\,\mathrm{rates}\,\mathrm{interpolation}=\mathrm{LogLinear}\right)\:$

$\mathrm{ForwardRate}\left(R\,0.\,0.5\right)$

$0.04000000000$

$\mathrm{ForwardRate}\left(R\,0.1\,0.5\right)$

$0.04205582119$

$\mathrm{ForwardRate}\left(R\,1.5\right)$

$0.08448956888$

$\mathrm{plots}\left[\mathrm{display}\right]\left(\mathrm{plot}\left('\mathrm{ForwardRate}'\left(R\,0.1\,t\right)\,t=0.5..2\,\mathrm{color}=\mathrm{blue}\,\mathrm{thickness}=3\right)\,\mathrm{plot}\left('\mathrm{ForwardRate}'\left(R\,0.3\,t\right)\,t=0.5..2\,\mathrm{color}=\mathrm{blue}\,\mathrm{thickness}=3\right)\,\mathrm{axes}=\mathrm{BOXED}\,\mathrm{gridlines}=\mathrm{true}\right)$

$\mathrm{R1}≔\mathrm{ZeroCurve}\left(0.05\,\mathrm{referencedate}=''Jan-05-2006''\right)\:$

$\mathrm{R1}\left(1.0\right)$

$0.05000000000$

$\mathrm{ForwardRate}\left(\mathrm{R1}\,1.0\right)$

$0.05000000000$

$\mathrm{ForwardRate}\left(\mathrm{R1}\,0.5\,1.5\right)$

$0.05000000000$

$\mathrm{ForwardRate}\left(\mathrm{R1}\,''Jan-05-2007''\right)$

$0.04999999999$

$T≔\mathrm{YearFraction}\left(''Jan-05-2006''\,''Jan-05-2007''\,\mathrm{R1}:-\mathrm{daycounter}\right)$

$T≔1.$

$\mathrm{R2}≔\mathrm{ZeroCurve}\left(0.05\,\mathrm{compounding}=\mathrm{Monthly}\,\mathrm{referencedate}=''Jan-05-2005''\right)\:$

$\mathrm{R2}\left(''Jan-05-2005''\right)$

$0.04989612178$

$\mathrm{R2}\left(1.0\right)$

$0.04989612178$

$\mathrm{ForwardRate}\left(\mathrm{R2}\,0.5\,1.0\right)$

$0.04989612178$

$\mathrm{rates}≔\left[0.02\,0.01\,0.04\,0.06\,0.07\right]\:$

$\mathrm{times}≔\left[0.\,0.5\,1.0\,1.5\,2.0\right]\:$

$\mathrm{R3}≔\mathrm{ZeroCurve}\left(\mathrm{times}\,\mathrm{rates}\right)\:$

$\mathrm{ForwardRate}\left(\mathrm{R3}\,0.5\,1.0\right)$

$0.07000000000$

Brigo, D., Mercurio, F., Interest Rate Models: Theory and Practice. New York:

Hull, J., Options, Futures, and Other Derivatives, 5th. edition. Upper Saddle River, New Jersey: Prentice Hall, 2003.

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

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