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.
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