The HullWhiteModel command creates a Hull-White model with the specified parameters. Under this model the short rate process $r\left(t\right)$ has the following dynamics with respect to the risk-neutral measure

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

$\mathrm{times}≔\left[0.08\,0.24\,0.48\,1.0\,2.0\,5.0\,10.0\,30.0\right]$

$\mathrm{times}≔\left[0.08\,0.24\,0.48\,1.0\,2.0\,5.0\,10.0\,30.0\right]$

$\mathrm{rates}≔\left[0.03\,0.032\,0.035\,0.04\,0.045\,0.05\,0.053\,0.055\right]$

$\mathrm{rates}≔\left[0.03\,0.032\,0.035\,0.04\,0.045\,0.05\,0.053\,0.055\right]$

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

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

$\mathrm{plot}\left(R\,0..30\,\mathrm{axes}=\mathrm{BOXED}\,\mathrm{thickness}=2\,\mathrm{gridlines}=\mathrm{true}\right)$

$M≔\mathrm{HullWhiteModel}\left(R\,1.0\,0.02\right)$

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

$X≔\mathrm{ShortRateProcess}\left(M\right)$

$X≔\mathrm{\_R}$

$\mathrm{PathPlot}\left(X\left(t\right)\,t=0..1\,\mathrm{timesteps}=50\,\mathrm{replications}=20\,\mathrm{axes}=\mathrm{BOXED}\,\mathrm{thickness}=2\,\mathrm{color}=\mathrm{red}..\mathrm{blue}\,\mathrm{gridlines}=\mathrm{true}\right)$

$T≔\mathrm{ShortRateTree}\left(M\,20\,20\right)$

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

$\mathrm{TreePlot}\left(T\,\mathrm{axes}=\mathrm{BOXED}\,\mathrm{thickness}=2\,\mathrm{gridlines}=\mathrm{true}\right)$

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.

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

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