The ParRate command calculates the implied par rate for a given sequence of payments at the given times.

The ParRate(termstructure, n, step, starttime, frequency) calling sequence calculates the interest rate that is equivalent to n payments every step years starting at starttime based on the given yield term structure. The optional frequency parameter can be used to specify the compounding frequency for the returned rate. By default, Annual frequency is used.

The ParRate(termstructure, paymenttimes, frequency) calling sequence is similar to the above except that in this case irregular payment times can be given.

The ParRate(termstructure, schedule, frequency) calling sequence will calculate the par rate for interest payments that occur according to the given schedule.

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

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

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

$R≔\mathrm{ZeroCurve}\left(\mathrm{times}\,\mathrm{rates}\,\mathrm{interpolation}=\mathrm{LogLinear}\,\mathrm{referencedate}=''January\; 05,\; 2006''\right)$

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

$\mathrm{ParRate}\left(R\,5\,1.0\,1.0\,\mathrm{Annual}\right)$

$0.2080324452$

$\frac{\mathrm{ParRate}\left(R\,5\,1.0\,1.0\,\mathrm{Monthly}\right)}{12}$

$0.2080324452$

$T≔\left[\mathrm{seq}\left(1.0+i\cdot 1.0\,i=0..5\right)\right]$

$T≔\left[1.0\,2.0\,3.0\,4.0\,5.0\,6.0\right]$

$\mathrm{ParRate}\left(R\,T\,\mathrm{Annual}\right)$

$0.2526682224$

$S≔\mathrm{Schedule}\left(''January\; 05,\; 2007''\,''January\; 05,\; 2008''\,\mathrm{Monthly}\right)$

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

$\mathrm{ParRate}\left(R\,S\,\mathrm{Monthly}\right)$

$0.1002412388$

Brigo, D., Mercurio, F., Interest Rate Models: Theory and Practice. New York: Springer-Verlag, 2001.

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

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

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