Three Make a Dynamic Smile – Unspanned Skewnessand Interacting Volatility Components in OptionValuation

We study a new class of three-factor affine option pricing models with interdependent volatilitydynamics and a stochastic skewness component unrelated to volatility shocks. Theseproperties are useful in order (i) to model a term structure of implied volatility skews moreconsistent with the data and (ii) to capture comovements of short and long term skews largelyunrelated to the volatility dynamics. We estimate our models using about fourteen years ofS&P 500 index option data and nd that on average they improve the out-of-sample pricingaccuracy of benchmark two- and three-factor affine models by 20%. Using an appropriatedecomposition of volatility and skewness, highlighting the main directions of improvementsproduced by our setting, we show that the enhanced t results from an improved modelingof the term structure of implied-volatility skews. The largest pricing improvements tendto concentrate during periods of nancial crises or market distress, suggesting volatilityunrelatedskewness as a potentially useful reduced-form risk factor for reproducing some ofthe crisis-related dynamics of index option smiles.[...]