# Explaining the Relationship of Expected Option Returns and Volatility Risk Premia

Alejandro Bernales and XiaoHua Chen^{*}

We study the expected leverage-adjusted returns on a single stock call and put portfolios, where we use a general equilibrium option pricing model under rational Bayesian learning. In a simulated market characterized by incomplete information and economic breaks (i.e. shocks), learning makes beliefs time-varying in ways that induce large and dynamic premiums in option prices and their implied volatilities. We show that the difference between implied volatility and realized volatility (hereafter volatility risk premia) significantly explains the expected leveraged-adjusted option returns. This implies that learning-based volatility risk premia captures jumps in stock price and volatility, that can be used to explain the puzzle of option returns found in the real markets.

Mathematics Subject Classification: 91C99 62X07

Keywords: Expected option returns; Volatility Risk Premia; Bayesian learning; option pricing model; Monte Carlo simulation

Minisymposion: Computational Optimization Methods in Statistics, Econometrics and Finance