Learning How to Smile : Can Rational Learning Explain the Predictable Dynamics in the Implied Volatility Surface?

We develop a general equilibrium asset pricing model under incomplete information and rational learning to explain the yet unexplained predictability of option prices. In our model, the fundamental dividend growth rate is unknown and subject to breaks, with time periods between breaks that follow a memory-less stochastic process. 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 in ways that induce large and dynamic risk premia in option prices and their implied volatilities. In addition, we find that learning generates different effects across option contracts with different strike prices and maturities. This induces realistic movements in the volatility surface implicit in option prices