Jump and Volatility Dynamics for the S&P 500: Evidence for Infinite-Activity Jumps with Non-Affine Volatility Dynamics from Stock and Option Markets*

Abstract

Relatively little is known about the empirical performance of infinite-activity Levy jump models, especially with non-affine volatility dynamics. We use extensive empirical data sets to study how infinite-activity Variance Gamma and Normal Inverse Gaussian (NIG) jumps with affine and non-affine volatility dynamics improve goodness of fit and option pricing performance. With Markov Chain Monte Carlo, different model specifications are estimated using the joint information of the S&P 500 index and the VIX. Our article provides clear evidence that a parsimonious non-affine model with NIG return jumps and a linear variance specification is particularly competitive, even during the recent crisis.