Euler-Maruyama Approximation for Mean-Reverting Regime Switching CEV Process

Abstract

The mean-reverting constant elasticity of variance (CEV) process with regime switching is one of the most successful continuous-time models of the short term rate, volatility, and other financial quantities. However, most SDEs with Markovian switching do not have explicit solutions. This paper obtains the Euler-Maruyama approximate solution for mean-reverting Regime Switching CEV processes and provides a detailed proof of the convergence of the EM approximate solution to the exact solution. In this paper, we investigate the Euler-Maruyama approximate solution of a stochastic differential equation, where we generalize the mean-reverting CEV process by replacing the constant parameters with the corresponding parameters modulated by a continuous-time, finite-state, Markov chain. This paper obtain the Euler-Maruyama approximate solution for mean-reverting Regime Switching CEV processes and provides a detailed proof of the strong convergence of the EM approximate solution to the exact solution. This paper is organized as follows. In Section II, we develop a mean-reverting CEV process with regime switching. The Euler-Maruyama approximate solution is provided in Section III. In Section IV, we provide a detailed proof of the strong convergence of the EM approximate solution to the exact solution. Conclusion is given in Section V.