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Journal of Applied Mathematics and Stochastic Analysis
Volume 2006 (2006), Article ID 80967, 20 pages

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.


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.