Capturing option anomalies with a variance-dependent pricing kernel

We develop a GARCH option model with a variance premium by combining the Heston-Nandi (2000) dynamic with a new pricing kernel that nests Rubinstein (1976) and Brennan (1979). 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 U-shaped. We present new semi-parametric evidence to con…firm 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.