Parametric Inference and Dynamic State Recovery from Option Panels

We develop a new parametric estimation procedure for option panels observed with error which relies on asymptotic approximations assuming an ever increasing set of observed option prices in the moneyness-maturity (cross-sectional) dimension, but with a fixed time span. We develop consistent estimators of the parameter vector and the dynamic realization of the state vector that governs the option price dynamics. The estimators converge stably to a mixed-Gaussian law and we develop feasible estimators for the limiting variance. We provide semi-parametric tests for the option price dynamics based on the distance between the spot volatility extracted from the options and the one obtained non-parametrically from high-frequency data on the underlying asset. We further construct new formal tests of the model fit for specific regions of the volatility surface and for the stability of the risk-neutral dynamics over a given period of time.