A GARCH Option Model with Variance-Dependent Pricing Kernel∗

We develop a GARCH option model with a variance premium by combining the HestonNandi (2000) dynamic with a new pricing kernel. While the pricing kernel is monotonic in the stock return and in variance, its projection onto the stock return is nonmonotonic. A negative variance premium makes it appear U-shaped. We present new semi-parametric evidence to confirm this U-shaped relationship between the risk-neutral and physical probability densities. The new pricing kernel substantially improves our ability to reconcile the time series properties of stock returns with the cross-section of option prices. It provides a unified explanation for the implied volatility puzzle, the overreaction of long-term options to changes in short-term variance, and the fat tails of the risk-neutral return distribution relative to the physical distribution. JEL Classification: G12