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December 2015 Uniform approximation of the Cox-Ingersoll-Ross process
Grigori N. Milstein, John Schoenmakers
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Adv. in Appl. Probab. 47(4): 1132-1156 (December 2015). DOI: 10.1239/aap/1449859803

Abstract

The Doss-Sussmann (DS) approach is used for uniform simulation of the Cox-Ingersoll-Ross (CIR) process. The DS formalism allows us to express trajectories of the CIR process through solutions of some ordinary differential equation (ODE) depending on realizations of a Wiener process involved. By simulating the first-passage times of the increments of the Wiener process to the boundary of an interval and solving the ODE, we uniformly approximate the trajectories of the CIR process. In this respect special attention is payed to simulation of trajectories near 0. From a conceptual point of view the proposed method gives a better quality of approximation (from a pathwise point of view) than standard, even exact, simulation of the stochastic differential equation at some deterministic time grid.

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Grigori N. Milstein. John Schoenmakers. "Uniform approximation of the Cox-Ingersoll-Ross process." Adv. in Appl. Probab. 47 (4) 1132 - 1156, December 2015. https://doi.org/10.1239/aap/1449859803

Information

Published: December 2015
First available in Project Euclid: 11 December 2015

zbMATH: 1335.65011
MathSciNet: MR3433299
Digital Object Identifier: 10.1239/aap/1449859803

Subjects:
Primary: 65C30
Secondary: 60H35

Keywords: Bessel function , confluent hypergeometric equation , Cox-Ingersoll-Ross process , Doss-Sussmann formalism

Rights: Copyright © 2015 Applied Probability Trust

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Vol.47 • No. 4 • December 2015
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