ParRate - Maple Help

Finance

 ParRate
 calculate an interest on par with a term structure

 Calling Sequence ParRate(termstructure, n, step, starttime, frequency) ParRate(termstructure, paymenttimes, frequency) ParRate(termstructure, schedule, frequency)

Parameters

 termstructure - yield term structure; term structure n - positive integer; number of payments step - positive; length of the interval between payments in years frequency - Annual, Bimonthly, EveryFourthMonth, Monthly, Quarterly, or Semiannual; payment frequency paymenttimes - list or Vector; payment times starttime - non-negative constant; start of payments schedule - schedule data structure; payment schedule

Description

 • 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.

Examples

 > $\mathrm{with}\left(\mathrm{Finance}\right):$
 > $\mathrm{rates}≔\left[0.02,0.01,0.04,0.06,0.07\right]:$
 > $\mathrm{times}≔\left[0.,0.5,1.0,1.5,2.0\right]:$
 > $R≔\mathrm{ZeroCurve}\left(\mathrm{times},\mathrm{rates},\mathrm{interpolation}=\mathrm{LogLinear},\mathrm{referencedate}="January 05, 2006"\right)$
 ${R}{≔}{\mathbf{module}}\left({}\right)\phantom{\rule[-0.0ex]{0.5em}{0.0ex}}{}\phantom{\rule[-0.0ex]{0.5em}{0.0ex}}{\mathbf{end module}}$ (1)
 > $\mathrm{ParRate}\left(R,5,1.0,1.0,\mathrm{Annual}\right)$
 ${0.2080324452}$ (2)
 > $\frac{\mathrm{ParRate}\left(R,5,1.0,1.0,\mathrm{Monthly}\right)}{12}$
 ${0.2080324452}$ (3)
 > $T≔\left[\mathrm{seq}\left(1.0+i\cdot 1.0,i=0..5\right)\right]$
 ${T}{≔}\left[{1.0}{,}{2.0}{,}{3.0}{,}{4.0}{,}{5.0}{,}{6.0}\right]$ (4)
 > $\mathrm{ParRate}\left(R,T,\mathrm{Annual}\right)$
 ${0.2526682224}$ (5)
 > $S≔\mathrm{Schedule}\left("January 05, 2007","January 05, 2008",\mathrm{Monthly}\right)$
 ${S}{≔}{\mathbf{module}}\left({}\right)\phantom{\rule[-0.0ex]{0.5em}{0.0ex}}{}\phantom{\rule[-0.0ex]{0.5em}{0.0ex}}{\mathbf{end module}}$ (6)
 > $\mathrm{ParRate}\left(R,S,\mathrm{Monthly}\right)$
 ${0.1002412388}$ (7)

References

 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.

Compatibility

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