Three make a dynamic smile – unspanned skewness and interacting volatility components in option valuation

We propose a new modeling approach to option valuation, in which the volatility and skewness of returns are functions of three distinct, but dependent, stochastic components: Two components modeling short and long run volatility risk and a third component capturing shocks to return skewness that are unspanned by shocks to volatility. The model state dynamics follows a matrix jump diffusion, provides efficient pricing formulae for plain vanilla options and nests a number of existing multi-factor affine models. We introduce dynamic interactions between the different components by relating the persistence and local variance of the volatility factors to the degree of return skewness, and vice versa. We estimate our model using S&P 500 index option data. We find that models with unspanned skewness components and dynamic interactions provide better pricing performance and a more accurate description of the joint dynamics of the implied volatility surface, both in-sample and out-of-sample. These findings support the use of option pricing models with (i) at least three distinct components driving the volatility and skewness of returns, (ii) skewness components that are not completely spanned by volatility shocks and (iii) interactions between the distinct component dynamics. JEL classification: