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Uniform approximation of the Cox-Ingersoll-Ross process

Part of: Stochastic analysis Probabilistic methods, simulation and stochastic differential equations

Published online by Cambridge University Press:  21 March 2016

Grigori N. Milstein  and
John Schoenmakers
Grigori N. Milstein*
Affiliation:
Ural Federal University
John Schoenmakers*
Affiliation:
Weierstrass Institute for Applied Analysis and Stochastics
*
∗ Postal address: Ural Federal University, Lenin Str. 51, 620083 Ekaterinburg, Russia.
∗∗ Postal address: Weierstrass Institute for Applied Analysis and Stochastics, Mohrenstrasse 39, 10117 Berlin, Germany. Email address: [email protected]
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Abstract

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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.

Keywords

Cox-Ingersoll-Ross processDoss-Sussmann formalismBessel functionconfluent hypergeometric equation

MSC classification

Primary: 65C30: Stochastic differential and integral equations
Secondary: 60H35: Computational methods for stochastic equations
Type
General Applied Probability
Information
Advances in Applied Probability , Volume 47 , Issue 4 , December 2015 , pp. 1132 - 1156
Copyright
Copyright © Applied Probability Trust 2015 

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