Assessing the quality of volatility estimators via option pricing

The aim of this paper is to measure and assess the accuracy of different volatility estimators based on high frequency data in an option pricing context. For this we use a stochastic volatility model based on Auto-Regressive-Gamma (ARG) dynamics for the volatility. First, ARG processes are presented both under historical and risk-neutral measure, in an affine stochastic discount factor framework. The model parameters are estimated exploiting the informative content of historical high frequency data. Secondly, option pricing is performed via Monte Carlo techniques. This framework allows us to measure the quality of different volatility estimators in terms of mispricing with respect to real option data, leaving to the ARG volatility model the role of a tool. The empirical analysis is conducted on European options written on S\&P500 index.