Relatively little is known about the empirical performance of infinite-activity Lévy 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.

This paper uses information on VIX to improve the empirical performance of GARCH models for pricing options on the S&P 500. In pricing multiple cross-sections of options, the models’ performance can clearly be improved by extracting daily spot volatilities from the series of VIX rather than by linking spot volatility with different dates by using the series of the underlying’s returns. Moreover, in contrast to traditional returns-based Maximum Likelihood Estimation (MLE), a joint MLE with returns and VIX improves option pricing performance, and for NGARCH, joint MLE can yield empirically almost the same out-of-sample option pricing performance as direct calibration does to in-sample options, but without costly computations. Finally, consistently with the existing research, this paper finds that non-affine models clearly outperform affine models.