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Beyond Stochastic Volatility and Jumps in Returns and Volatility

2012; Taylor & Francis; Volume: 31; Issue: 1 Linguagem: Inglês

10.1080/07350015.2013.747800

1537-2707

Garland Durham, Yang‐Ho Park,

Financial Markets and Investment Strategies

Abstract While a great deal of attention has been focused on stochastic volatility in stock returns, there is strong evidence suggesting that return distributions have time-varying skewness and kurtosis as well. Under the risk-neutral measure, for example, this can be observed from variation across time in the shape of Black–Scholes implied volatility smiles. This article investigates model characteristics that are consistent with variation in the shape of return distributions using a stochastic volatility model with a regime-switching feature to allow for random changes in the parameters governing volatility of volatility, leverage effect, and jump intensity. The analysis consists of two steps. First, the models are estimated using only information from observed returns and option-implied volatility. Standard model assessment tools indicate a strong preference in favor of the proposed models. Since the information from option-implied skewness and kurtosis is not used in fitting the models, it is available for diagnostic purposes. In the second step of the analysis, regressions of option-implied skewness and kurtosis on the filtered state variables (and some controls) suggest that the models have strong explanatory power for these characteristics. KEY WORDS: Jump intensityLeverage effectOption pricingRegime switchingReturn distributionsSkewnessStock price dynamics ACKNOWLEDGMENTS We are grateful for the helpful comments and suggestions of Jonathan Wright (the editor), two anonymous referees, David Bates, Peter Chrisoffersen, Jakša Cvitanić, John Geweke, Kris Jacobs, Bjorn Jorgensen, Yujin Oh, Mike Stutzer, Pascale Valery, and seminar participants at the University of Colorado, HEC Montreal, Eastern Finance Association 2010 Annual Meetings, 2010 NBER Summer Institute Working Group on Forecasting and Empirical Methods, and Front Range Finance Seminar. Disclaimer: The analysis and conclusions set forth are those of the authors and do not indicate concurrence by other members of the research staff or the Board of Governors.