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Journal of Probability and Statistics
Volume 2015, Article ID 513137, 20 pages
Research Article

Approximating Explicitly the Mean-Reverting CEV Process

Department of Mathematics, University of the Aegean, Karlovassi, 83 200 Samos, Greece

Received 2 September 2015; Revised 13 October 2015; Accepted 15 October 2015

Academic Editor: Steve Su

Copyright © 2015 N. Halidias and I. S. Stamatiou. 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.


We are interested in the numerical solution of mean-reverting CEV processes that appear in financial mathematics models and are described as nonnegative solutions of certain stochastic differential equations with sublinear diffusion coefficients of the form where . Our goal is to construct explicit numerical schemes that preserve positivity. We prove convergence of the proposed SD scheme with rate depending on the parameter . Furthermore, we verify our findings through numerical experiments and compare with other positivity preserving schemes. Finally, we show how to treat the two-dimensional stochastic volatility model with instantaneous variance process given by the above mean-reverting CEV process.