Estimation of Generalized Diffusions from Option Prices

Abstract

This paper develops option-based estimators of the diffusion using the Estimating Function approach. The resulting estimators have a generic structure that applies to a wide class of state-time separable diffusions found in option pricing models. Our methodology differs from the related literature in a number of ways. First, inferences regarding the diffusion are made jointly from option and asset prices and Estimating Function theory identifies the optimal estimating equation for the estimators. Second, the method is distribution-free in the sense that estimation of the diffusion's transition density is not required. Lastly, the proposed option diffusion estimators are robust to distributional assumptions on the underlying asset prices (e.g. log-normality) as their asymptotic convergence and normality is established under conditional first and second moment assumptions. Monte-Carlo analysis verifies the accuracy and efficiency of the option diffusion estimators and resolves important sample design issues. Applications of the proposed option diffusion estimators to empirical option pricing, quantifying divergence between option and asset prices, and investment strategies are discussed.