Illuminating the Pricing Kernels: Short-Term and Long-Term Index Option Returns

The shape of the pricing kernel has important implications for expected option returns. We shed light on the pricing kernel puzzle (i.e., mixed results regarding the shape of the pricing kernel) by examining S&P 500 index option returns and empirical pricing kernels across a wide range of expiration dates (from 1 month to 1 year). We document that at short (long) maturities, out-of-the-money call option returns are negative (positive) and decrease (increase) with the strike price. At short maturities, empirical pricing kernels predominantly exhibit a W-shape, while this pattern becomes less pronounced, evolving toward a monotonically decreasing curve at longer maturities. Our study suggests that the shape of pricing kernels and call option returns varies with option maturities, reflecting investors' heterogeneous beliefs about index returns across different time horizons.