Learning to smile: Can rational learning explain predictable dynamics in the implied volatility surface?

Abstract

We develop a general equilibrium asset pricing model under incomplete information and rational learning in order to understand the unexplained predictability of option prices. In our model, the fundamental dividend growth rate is unknown and subject to breaks. Immediately after a break, there is insufficient information to price option contracts accurately. However, as new information arrives, a representative Bayesian agent recursively learns about the parameters of the process followed by fundamentals. We show that learning makes beliefs time-varying and generates predictability patterns across option contracts with different strike prices and maturities; as a result, the implied movements in the implied volatility surface resemble those observed empirically.