Do Stock Prices and Volatility Jump? Reconciling Evidence from Spot and Option Prices

This paper studies the empirical performance of jump-diffusion models that allow for stochastic volatility and correlated jumps affecting both prices and volatility. The results show that the models in question provide reasonable fit to both option prices and returns data in the in-sample estimation period. This contrasts with previous findings where stochastic volatility paths are found to be too smooth relative to the option implied dynamics. While the models perform well during the high volatility estimation period, they tend to overprice long dated contracts out-of-sample. This evidence points towards a too simplistic specification of the mean dynamics of volatility.