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

This paper studies the empirical performance of jump-di usion models that allow for stochastic volatility and correlated jumps a ecting both prices and volatility. We propose a simulation method for conducting likelihood based inference from a panel of options data, as well as returns data simultaneously. Empirical results from S&P 500 returns/options di er from the current literature in several important ways. First, we cannot replicate previous ndings of an internal inconsistency between parameter-estimates and the latent spot-volatility process. Second, while the jump models do not provide better t to option prices than the basic stochastic volatility model does, the jump-in-volatility model provides substantially better t to the time-series data. Our results also suggest that time variation in relative option prices, as well as systematic variability in returns, can be adequately captured by a common stochastic volatility compo-