Option Implied VIX, Skew and Kurtosis Term Structures

Comparisons are made of the Chicago Board of Options Exchange (CBOE) skew index with those derived from parametric skews of bilateral gamma models and from the differentiation of option implied characteristic exponents. Discrepancies can be due to strike discretization in evaluating prices of powered returns. The remedy suggested employs a finer and wider set of strikes obtaining additional option prices by interpolation and extrapolation of implied volatilities. Procedures of replicating powered return claims are applied to the fourth power and the derivation of kurtosis term structures. Regressions of log skewness and log excess kurtosis on log maturity confirm the positivity of decay in these higher moments. The decay rates are below those required by processes of independent and identically distributed increments.