Three Make a Dynamic Smile - Unspanned Skewness and Interacting Volatility Components in Option Valuation

Abstract

We study a new class of three-factor affine option pricing models with interdependent volatility dynamics and a stochastic skewness component unrelated to volatility shocks. These properties are useful in order (i) to model a term structure of implied volatility skews more consistent with the data and (ii) to capture comovements of short and long term skews largely unrelated to the volatility dynamics. We estimate our models using about fourteen years of S&P 500 index option data and find that on average they improve the out-of-sample pricing accuracy of benchmark two- and three-factor affine models by 20%. Using an appropriate decomposition of volatility and skewness, highlighting the main directions of improvements produced by our setting, we show that the enhanced fit results from an improved modeling of the term structure of implied-volatility skews. The largest pricing improvements tend to concentrate during periods of financial crises or market distress, suggesting volatility- unrelated skewness as a potentially useful reduced-form risk factor for reproducing some of the crisis-related dynamics of index option smiles.

Keywords: Option Pricing, Stochastic Volatility, Stochastic Leverage, Short and Long Run Volatility Risk, Matrix Affine Jump Diffusions

JEL Classification: G10, G12, G13