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

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  • Guidolin, Massimo
  • Timmermann, Allan G

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.

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Bibliographic Info

Paper provided by C.E.P.R. Discussion Papers in its series CEPR Discussion Papers with number 3005.

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Date of creation: Oct 2001
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Handle: RePEc:cpr:ceprdp:3005

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Keywords: Bayesian learning; Black-Scholes option pricing model; option prices;

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References

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  1. Jin-Chuan Duan, 1995. "The Garch Option Pricing Model," Mathematical Finance, Wiley Blackwell, vol. 5(1), pages 13-32.
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  20. Mark Rubinstein., 1994. "Implied Binomial Trees," Research Program in Finance Working Papers RPF-232, University of California at Berkeley.
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  32. repec:cup:etheor:v:11:y:1995:i:1:p:151-89 is not listed on IDEAS
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  34. Rubinstein, Mark, 1994. " Implied Binomial Trees," Journal of Finance, American Finance Association, vol. 49(3), pages 771-818, July.
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