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Finance

 ShortRateProcess
 return a stochastic process that governs a short rate in the given model

 Calling Sequence ShortRateProcess(model)

Parameters

 model - short-rate model data structure; short-rate model

Description

 • The ShortRateProcess command returns a stochastic process that represents the instantaneous spot rate in the given short-rate model.

Examples

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

First define a Vasicek model with parameters ${r}_{0}=0.03$, $\mathrm{\mu }=0.05$, $\mathrm{\theta }=0.3$ and $\mathrm{\sigma }=0.002$.

 > $M≔\mathrm{VasicekModel}\left(0.03,0.05,0.3,0.002\right)$
 ${M}{:=}{\mathbf{module}}\left({}\right)\phantom{\rule[-0.0ex]{0.5em}{0.0ex}}{}\phantom{\rule[-0.0ex]{0.5em}{0.0ex}}{\mathbf{end module}}$ (1)

The following is the corresponding stochastic process.

 > $X≔\mathrm{ShortRateProcess}\left(M\right)$
 ${X}{:=}{\mathrm{_X}}$ (2)
 > $\mathrm{PathPlot}\left(X\left(t\right),t=0..1,\mathrm{timesteps}=50,\mathrm{replications}=20,\mathrm{axes}=\mathrm{BOXED},\mathrm{thickness}=3,\mathrm{color}=\mathrm{red}..\mathrm{blue},\mathrm{gridlines}=\mathrm{true}\right)$
 > $\mathrm{PathPlot}\left({ⅇ}^{{{∫}}_{0}^{t}X\left(u\right)\phantom{\rule[-0.0ex]{0.3em}{0.0ex}}{ⅆ}u},t=0..1,\mathrm{timesteps}=50,\mathrm{replications}=20,\mathrm{axes}=\mathrm{BOXED},\mathrm{thickness}=3,\mathrm{color}=\mathrm{red}..\mathrm{blue},\mathrm{gridlines}=\mathrm{true}\right)$

References

 Brigo, D., Mercurio, F., Interest Rate Models: Theory and Practice, New York: Springer-Verlag, 2001.
 Glasserman, P., Monte Carlo Methods in Financial Engineering, New York: Springer-Verlag, 2004.
 Hull, J., Options, Futures, and Other Derivatives, 5th. edition. Upper Saddle River, New Jersey: Prentice Hall, 2003.
 Vasicek, O.A., An Equilibrium Characterization of the Term Structure, Journal of Financial Economics, 5 (1977), pp 177-188.

Compatibility

 • The Finance[ShortRateProcess] command was introduced in Maple 15.
 • For more information on Maple 15 changes, see Updates in Maple 15.

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