DP3005 Option Prices under Bayesian Learning: Implied Volatility Dynamics and Predictive Densities

Author(s): Massimo Guidolin, Allan Timmermann
Publication Date: October 2001
Keyword(s): Bayesian learning, Black-Scholes option pricing model, option prices
JEL(s): D83, G12
Programme Areas: Financial Economics
Link to this Page: cepr.org/active/publications/discussion_papers/dp.php?dpno=3005

This Paper shows that many of the empirical biases of the Black and Scholes option pricing model can be explained by Bayesian learning effects. In the context of an equilibrium model where dividend news evolves on a binomial lattice with unknown but recursively updated probabilities, we derive closed-form pricing formulas for European options. Learning is found to generate asymmetric skews in the implied volatility surface and systematic patterns in the term structure of option prices. Data on S&P 500 index option prices is used to back out the parameters of the underlying learning process and to predict the evolution in the cross-section of option prices. The proposed model leads to lower out-of-sample forecast errors and smaller hedging errors than a variety of alternative option pricing models, including Black-Scholes and a GARCH model.