Implied volatility and skewness surface

The Homoscedastic Gamma (HG) model characterizes the distribution of returns by its mean, variance and an independent skewness parameter. The HG model preserves the parsimony and the closed form of the Black–Scholes–Merton (BSM) while introducing the implied volatility (IV) and skewness surface. Varying the skewness parameter of the HG model can restore the symmetry of IV curves. Practitioner’s variants of the HG model improve pricing (in-sample and out-of-sample) and hedging performances relative to practitioners’ BSM models, with as many or less parameters. The pattern of improvements in Delta-Hedged gains across strike prices accord with predictions from the HG model. These results imply that expanding around the Gaussian density does not offer sufficient flexibility to match the skewness implicit in options. Consistent with the model, we also find that conditioning on implied skewness increases the predictive power of the volatility spread for excess returns.