Bayesian Approach to Markov Switching Stochastic Volatility Model with Jumps

Abstract

This article proposes a new stochastic volatility model incorporating both the jumps in price process and the structural changes in volatility. Bayesian approach based on data augmentation and MCMC algorithm is adopted to estimate the model. Finally, the empirical study shows that the proposed model can identify the jumps and the volatility structure simultaneously. Moreover, high volatility state portends the large jumps and then the tranquil low volatility state follows. This model first provides a useful tool to analyze the volatility structure of market combining with the jumps during the periods of drastic fluctuation.

Keywords:

• Bayesian inference
• Jumps
• Markov switching
• Monte Carlo Markov Chain
• Stochastic volatility

Mathematics Subject Classification:

• 62F15
• 62M10

Acknowledgments

This research was supported in part by Ministry of Education Humanities Social Science Key Research Institute in University Foundation (07JJD910244) and NSFC (71071155, 10771214), the Fundamental Research Funds for the Central Universities, and the Research Funds of Renmin University of China (11XNI008, 10XNL007), and the Graduate Research Foundation of RUC (22396177).