GMM Estimation of Stochastic Volatility Models Using Transform-Based Moments of Derivatives Prices

Abstract

Derivatives, especially equity and volatility options, contain valuable and oftentimes essential information for estimating stochastic volatility models. Absent strong assumptions, their typically highly nonlinear pricing dependence on the state vector prevents or at least severely impedes their inclusion into standard estimation approaches. This paper develops a novel and unified methodology to incorporate moments involving derivatives prices into a GMM estimation procedure. Invoking new results from generalized transform analysis, we derive analytically tractable expressions for exact moments and devise a computationally attractive approximation procedure. We exemplify our methodology with an estimation problem that jointly accounts for stock returns as well as prices of equity and volatility options. Finally, we provide numerical results that support the effectiveness of our methodology.