Approximating explicitly the mean reverting CEV process
For researchers in financial mathematics, this provides an explicit positivity-preserving scheme for a class of stochastic differential equations, though it is an incremental extension of prior work.
The paper proposes an explicit numerical scheme for mean reverting CEV processes that preserves positivity, proving convergence with a rate depending on the parameter q, and validates it through numerical experiments.
In this paper we want to exploit further the semi-discrete method appeared in Halidias and Stamatiou (2015). We are interested in the numerical solution of mean reverting CEV processes that appear in financial mathematics models and are described as non negative solutions of certain stochastic differential equations with sub-linear diffusion coefficients of the form $(x_t)^q,$ where $\frac{1}{2}<q<1.$ 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 $q.$ Furthermore, we verify our findings through numerical experiments and compare with other positivity preserving schemes. Finally, we show how to treat the whole two-dimensional stochastic volatility model, with instantaneous variance process given by the above mean reverting CEV process.