Realizing Smiles: Pricing Options with Realized Volatility

We develop a stochastic volatility option pricing model that exploits the informative content of historical high frequency data. Using the Two Scales Realized Volatility as a proxy for the unobservable returns volatility, we propose a simple (affine) but effective long-memory process: the Heterogeneous Auto-Regressive Gamma (HARG) model. This discrete–time process, combined with an exponential affine stochastic discount factor, leads to a completely tractable risk-neutral dynamics. The explicit change of probability measure obtained within this framework allows the estimation of the risk-neutral parameters directly under the physical measure, leaving only one free parameters to be calibrated. An empirical analysis on S&P 500 option index shows that the proposed model outperforms competing GARCH models, being able to better capture the overall shape and dynamics of the implied volatility surface.