define Cox-Ingersoll-Ross interest rate model
CoxIngersollRossModel(r, theta, kappa, sigma, x0)
initial term structure
long term mean level
speed of reversion
The CoxIngersollRossModel command creates a Cox-Ingersoll-Ross 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 θ, κ, σ, and x0 are non-negative constants and W(t) is a Wiener process modeling the random market risk factor.
It is reasonable to require that σ2<2⁢κ⁢θ.
First define a Cox-Ingersoll-Ross model with parameters r0=0.03, θ=0.05, κ=0.5, σ=0.002, and x0=0.1.
M ≔ CoxIngersollRossModel⁡ZeroCurve⁡0.03,0.05,0.5,0.002,0.1
M ≔ moduleend module
Here is the corresponding short rate tree.
T ≔ ShortRateTree⁡M,5,40
T ≔ moduleend module
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.
The Finance[CoxIngersollRossModel] command was introduced in Maple 15.
For more information on Maple 15 changes, see Updates in Maple 15.
Download Help Document
What kind of issue would you like to report? (Optional)