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Uniform approximation of the Cox–Ingersoll–Ross process via exact simulation at random times

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

Published online by Cambridge University Press:  11 January 2017

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: schoenma@wias-berlin.de
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Abstract

In this paper we uniformly approximate the trajectories of the Cox–Ingersoll–Ross (CIR) process. At a sequence of random times the approximate trajectories will be even exact. In between, the approximation will be uniformly close to the exact trajectory. From a conceptual point of view, the proposed method gives a better quality of approximation in a path-wise sense than standard, or even exact, simulation of the CIR dynamics at some deterministic time grid.

Keywords

Cox–Ingersoll–Ross processSturm–Liouville problemBessel functionconfluent hypergeometric equation

MSC classification

Primary: 65C30: Stochastic differential and integral equations
Secondary: 60H35: Computational methods for stochastic equations
Type
Research Article
Information
Advances in Applied Probability , Volume 48 , Issue 4 , December 2016 , pp. 1095 - 1116
Copyright
Copyright © Applied Probability Trust 2017 

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