Journal of Applied Mathematics and Stochastic Analysis
Volume 2006 (2006), Article ID 80967, 20 pages
doi:10.1155/JAMSA/2006/80967
Euler-Maruyama approximations in mean-reverting
stochastic volatility model under regime-switching
1Department of Statistics and Modelling
Science, University of Strathclyde, Glasgow G1 1XH, Scotland, United Kingdom
2Department of Mathematics, School of Physical
Sciences, University of Wales Swansea, Swansea SA2 8PP, Wales, United Kingdom
Received 28 December 2005; Revised 9 February 2006; Accepted 9 February 2006
Copyright © 2006 Xuerong Mao et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Abstract
Stochastic differential equations (SDEs) under regime-switching
have recently been developed to model various financial
quantities. In general, SDEs under regime-switching have no
explicit solutions, so numerical methods for approximations have
become one of the powerful techniques in the valuation of
financial quantities. In this paper, we will concentrate on the
Euler-Maruyama (EM) scheme for the typical hybrid mean-reverting
θ-process. To overcome the mathematical difficulties
arising from the regime-switching as well as the non-Lipschitz
coefficients, several new techniques have been developed in this
paper which should prove to be very useful in the numerical
analysis of stochastic systems.