Further empirical evidence on stochastic volatility models with jumps in returns

Abstract

Using the Efficient Method of Moments we estimate a continuous time diffusion for the stochastic volatility of some international stock market indices that allows for possible jumps in returns. These jumps are needed for a sensible characterization of the dynamics of the distribution of returns, even under stochastic volatility. Although the stochastic volatility model with jumps in returns tends to exaggerate the negative skewness relative to the sample moments, the inclusion of jumps strongly improves the ability of the model to replicate sample kurtosis. This contrasts with the failure of the pure stochastic volatility model in generating high enough kurtosis. Our results extend the limited available evidence from the U.S. market to several European stock market indices.