The VasicekModel command creates a Vasicek 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

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

$\mathrm{model}≔\mathrm{VasicekModel}\left(0.03\,0.05\,0.3\,0.02\right)$

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

$r≔\mathrm{ShortRateProcess}\left(\mathrm{model}\right)$

$r≔\mathrm{\_X0}$

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

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

$\mathrm{tree}≔\mathrm{ShortRateTree}\left(\mathrm{model}\,20\,20\right)$

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

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

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

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

$\mathrm{discount}≔\mathrm{DiscountBondPrice}\left(\mathrm{model}\,0.03\,\mathrm{times}\right)$

$\mathrm{discount}≔\left[\begin{array}{cccccccc}0.997583909664655& 0.992659223166232& 0.985060167620859& 0.967860170077199& 0.932792565257669& 0.822762710983556& 0.653892081277046& 0.252136624704580\end{array}\right]$

$\mathrm{term\_structure}≔\mathrm{DiscountCurve}\left(\mathrm{times}\,\mathrm{convert}\left(\mathrm{discount}\,'\mathrm{list}'\right)\right)$

$\mathrm{term\_structure}≔\mathbf{module}\left(\right)\mathbf{end\; module}$

$\mathrm{plot}\left(\mathrm{term\_structure}\,0.1..30\,\mathrm{thickness}=2\,\mathrm{axes}=\mathrm{BOXED}\,\mathrm{gridlines}=\mathrm{true}\right)$

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[VasicekModel] command was introduced in Maple 15.

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