create Hull-White interest rate model
HullWhiteModel(theta, alpha, sigma)
observed term structure of interest rates
speed of mean reversion
The HullWhiteModel command creates a Hull-White model with the specified parameters. Under this model the short rate process r⁡t has the following dynamics with respect to the risk-neutral measure
where α and σ are non-negative constants and W(t) is a Wiener process modeling the random market risk factor.
times ≔ 0.08,0.24,0.48,1.0,2.0,5.0,10.0,30.0
rates ≔ 0.03,0.032,0.035,0.04,0.045,0.05,0.053,0.055
R ≔ ZeroCurve⁡times,rates
M ≔ HullWhiteModel⁡R,1.0,0.02
X ≔ ShortRateProcess⁡M
Here is the corresponding short-rate tree.
T ≔ ShortRateTree⁡M,20,20
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.
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