Empirical Performance and Asset Pricing in Hidden Markov Models

Abstract

To improve the empirical performance of the Black-Scholes model, many alternative models have been proposed to address leptokurtic feature, volatility smile, and volatility clustering effects of the asset return distributions. However, analytical tractability remains a problem for most alternative models. In this article, we study a class of hidden Markov models including Markov switching models and stochastic volatility models, that can incorporate leptokurtic feature, volatility clustering effects, as well as provide analytical solutions to option pricing. We show that these models can generate long memory phenomena when the transition probabilities depend on the time scale. We also provide an explicit analytic formula for the arbitrage-free price of the European options under these models. The issues of statistical estimation and errors in option pricing are also discussed in the Markov switching models.

Keywords:

• Markov switching model
• Stochastic volatility model
• Leptokurtic
• Cluster phenomenon
• Long memory
• Volatility smile
• European options
• Likelihood estimation
• EM algorithm

Acknowledgments

The first author's research partially supported by NSC 91-2118-M-001-016. The second author's research partially supported by Hong Kong Research Grant Council.