Realizing Smiles: Options Pricing with Realized Volatility

We develop a discrete-time stochastic volatility option pricing model, which exploits the informationcontained in high-frequency data. The Realized Volatility (RV) is used as a proxy of the unobservablelog-returns volatility. We model its dynamics by a simple but effective long-memory process: The LeverageHeterogeneous Auto-Regressive Gamma (HARGL) process. The discrete-time specification and theuse of the RV allows us to easily estimate the model using observed historical data. Assuming a standardexponentially affine stochastic discount factor, we obtain a fully analytic change of measure. An extensiveempirical analysis of S&P 500 index options illustrates that our approach significantly outperformscompeting time-varying (i.e. GARCH-type) and stochastic volatility pricing models. The pricing improvementcan be ascribed to: (i) The direct use of the RV, which provides a precise and fast-adapting measureof the unobserved underlying volatility; (ii) the specification of our model, which is able to accuratelyreproduce the implied volatility term structure.[...]