Approximating Explicitly the Mean-Reverting CEV Process

N. Halidias and I. S. Stamatiou

Journal of Probability and Statistics, 2015, vol. 2015, 1-20

Abstract:

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.

Date: 2015
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jnljps:513137

DOI: 10.1155/2015/513137

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