Beyond Stochastic Volatility and Jumps in Returns and Volatility

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.