Markov Regime Switching of Stochastic Volatility Lévy Model on Approximation Mode

Abstract

This paper deals with financial modeling to describe the behavior of asset returns, through consideration of economic cycles together with the stylized empirical features of asset returns such as fat tails. We propose that asset returns are modeled by a stochastic volatility Lévy process incorporating a regime switching model. Based on the risk-neutral approach, there exists a large set of candidates of martingale measures due to the driving of a stochastic volatility Lévy process in the proposed model which renders the market incomplete in general. We first establish an equivalent martingale measure for the proposed model introduced in risk-neutral version. Regime switching of stochastic volatility Lévy process is employed in an approximation mode for model calibration and the calibration of parameters model done based on EM algorithm. Finally, some empirical results are illustrated via applications to the Bangkok Stock Exchange of Thailand index.