Learning and forecasts about option returns through the volatility risk premium

Abstract

We use learning in an equilibrium model to explain the puzzling predictive power of the volatility risk premium ( V RP) for option returns. In the model, a representative agent fol- lows a rational Bayesian learning process in an economy under incomplete information with the objective of pricing options. We show that learning induces dynamic differences between probability measures P and Q , which produces predictability patterns from the VRP for option returns. The forecasting features of the VRP for option returns, obtained through our model, exhibit the same behaviour as those observed in an empirical analysis with S&P 500 index options.