Skewness Correction for Asset Pricing

It is shown that, for CRRA agents, the sensitivity of risk correction for any cumulant depends on the cumulant of the next order. This result is then used to derive some interesting approximations for variance and skewness correction. The first corollary is that negative skewness alone leads to higher variance swap rates since the variance swap contract provides insurance against sudden market drops. Thus, high variance swap rates are not necessarily an indication of high variance risk premia. When the results are extended to the multifactor case, we are able to disentangle the swap rate premia into their skewness and stochastic variance premia components. Finally, we contribute to the understanding of option skews by showing that only 1-u percent of excess kurtosis contributes to negative skewness correction, where u is a newly introduced statistic that normalizes skewness with kurtosis