Uniform approximation of the Cox-Ingersoll-Ross process via exact simulation at random times. (English) Zbl 1362.65016

Milstein, Grigori N.; Schoenmakers, John

Adv. Appl. Probab. 48, No. 4, 1095-1116 (2016).

The authors develop an alternative to their previous method of approximating the Cox-Ingersoll-Ross (CIR) stochastic process that arises in finance. This new method uses squared Bessel processes to obtain approximations of the CIR process and can be applied in the cases not covered by their previous method. Exact values of the CIR process are simulated at random exactly simulated times and error of the approximations between these times is shown to be uniformly small. Numerical implementation of the method is discussed.

Reviewer: Melvin D. Lax (Long Beach)

MSC:

65C30	Numerical solutions to stochastic differential and integral equations
60H35	Computational methods for stochastic equations (aspects of stochastic analysis)
60H10	Stochastic ordinary differential equations (aspects of stochastic analysis)
34F05	Ordinary differential equations and systems with randomness
91G60	Numerical methods (including Monte Carlo methods)
34B24	Sturm-Liouville theory

Keywords:

Cox-Ingersoll-Ross process; Sturm-Liouville problem; Bessel function; confluent hypergeometric equation; numerical example