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

The ZeroRate command returns the zero interest rate for the maturity maturitytime or maturitydate based on the specified term structure. 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.

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

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

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

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

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

$0.04000000000$

$\mathrm{ZeroRate}\left(R\,1.0\right)$

$0.06000000000$

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

$0.07000000000$

$\mathrm{plot}\left('\mathrm{ZeroRate}'\left(R\,t\right)\,t=0.5..2\,\mathrm{color}=\mathrm{blue}\,\mathrm{thickness}=3\,\mathrm{axes}=\mathrm{BOXED}\,\mathrm{gridlines}=\mathrm{true}\right)$

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

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

$0.05000000000$

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

$0.05000000000$

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

$0.05000000000$

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

$0.05000000000$

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

$T≔1.$

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

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

$0.04989612178$

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

$0.04989612178$

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

$0.04989612178$

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

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

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

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

$0.04000000000$

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[ZeroRate] command was introduced in Maple 15.

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