Option Prices Under Bayesian Learning: Implied Volatility Dynamics and Predictive Densities

61 Pages Posted: 1 Nov 2001

See all articles by Allan Timmermann

Allan Timmermann

UCSD ; Centre for Economic Policy Research (CEPR)

Massimo Guidolin

Bocconi University, Dept. of Finance; Bocconi University - CAREFIN - Centre for Applied Research in Finance

Multiple version iconThere are 3 versions of this paper

Date Written: October 2001

Abstract

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.

Keywords: Option prices, Black-Scholes option pricing model, Bayesian learning

JEL Classification: D83, G12

Suggested Citation

Timmermann, Allan and Guidolin, Massimo, Option Prices Under Bayesian Learning: Implied Volatility Dynamics and Predictive Densities (October 2001). Available at SSRN: https://ssrn.com/abstract=288583

Allan Timmermann

UCSD ( email )

9500 Gilman Drive
La Jolla, CA 92093-0553
United States
858-534-0894 (Phone)

HOME PAGE: http://rady.ucsd.edu/people/faculty/timmermann/

Centre for Economic Policy Research (CEPR)

London
United Kingdom

Massimo Guidolin (Contact Author)

Bocconi University, Dept. of Finance ( email )

Via Roentgen, 1
2nd floor
Milan, MI 20136
Italy

Bocconi University - CAREFIN - Centre for Applied Research in Finance

Via Sarfatti 25
Milan, 20136
Italy

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