The Shape of the Pricing Kernel and Expected Option Returns

A growing literature analyzes the cross-section of single stock option returns, virtually always under the (implicit or explicit) assumption of a monotonically decreasing pricing kernel. Using option returns, we non-parametrically provide significant and robust evidence that the pricing kernel as a function of single stock returns is indeed U-shaped. This shape of the pricing kernel has strong implications for the impact of volatility on expected options returns. For example, we show both theoretically and empirically that higher volatility can increase or decrease expected call option returns, depending on moneyness. Furthermore, on the basis of a U-shaped pricing kernel, we shed new light on some recent findings from the literature on expected option returns, such as anomalies related to ex-ante option return skewness and to lottery characteristics of the underlying stock