Moment Risk Premiums in Option Markets: On Measurement, Structure, and Investment Implications

Abstract

This paper studies quantile-based moment premiums. The quantile-based approach delivers robust and flexible alternatives to premiums for variance, skewness and kurtosis risk and enhances our understanding of the pricing of risks in derivatives markets. To quantify these premiums, the paper introduces a new class of synthetic derivatives contracts: quantile swaps. Such contracts mimic quantile-based moment measures from robust statistics. An empirical study of index options detects two distinct premiums for dispersion and asymmetry, but no premium for steepness.The premium for dispersion can be explained by traditional moment risk premiums, whereas the asymmetry premium is a novel premium that our approach is able to detect. Moreover, we disaggregate the overall premiums into upside and downside premiums. The downside dispersion premium is not restricted to the lower tail but is also observed in the center of the distribution. However, at the center, this downside premium is partly offset by an upside discount, explaining why the overall premium is mainly a tail effect. Overall, as some of our findings differ markedly from results obtained with traditional moment swaps, they are a warning to interpret moment premiums cautiously.