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

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Author Info
Allan Timmermann ()
Massimo Guidolin

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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 evolve 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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Paper provided by Financial Markets Group in its series FMG Discussion Papers with number dp397.

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Date of creation: Nov 2001
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Handle: RePEc:fmg:fmgdps:dp397

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References listed on IDEAS
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
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    Other versions:
  5. Harrison, J. Michael & Kreps, David M., 1979. "Martingales and arbitrage in multiperiod securities markets," Journal of Economic Theory, Elsevier, vol. 20(3), pages 381-408, June. [Downloadable!] (restricted)
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  7. Mark Rubinstein., 1994. "Implied Binomial Trees," Research Program in Finance Working Papers RPF-232, University of California at Berkeley. [Downloadable!]
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  16. Cox, John C. & Ross, Stephen A. & Rubinstein, Mark, 1979. "Option pricing: A simplified approach," Journal of Financial Economics, Elsevier, vol. 7(3), pages 229-263, September. [Downloadable!] (restricted)
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  22. Bossaerts, Peter, 1995. "The Econometrics of Learning in Financial Markets," Econometric Theory, Cambridge University Press, vol. 11(01), pages 151-189, February. [Downloadable!]
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  24. Black, Fischer & Scholes, Myron S, 1973. "The Pricing of Options and Corporate Liabilities," Journal of Political Economy, University of Chicago Press, vol. 81(3), pages 637-54, May-June. [Downloadable!] (restricted)
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Cited by:
(explanations, Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.)

  1. Carsten Krabbe Nielsen, 2004. "Rational overconfidence and excess volatility in General Equilibrium," Econometric Society 2004 Australasian Meetings 279, Econometric Society. [Downloadable!]
  2. Massimo Guidolin & Allan Timmerman, 2005. "Properties of equilibrium asset prices under alternative learning schemes," Working Papers 2005-009, Federal Reserve Bank of St. Louis. [Downloadable!]
    Other versions:
  3. Laurent E. Calvet & Adlai J. Fisher, 2005. "Multifrequency News and Stock Returns," NBER Working Papers 11441, National Bureau of Economic Research, Inc. [Downloadable!] (restricted)
    Other versions:
  4. Carsten Krabbe Nielsen, 2004. "Rational overconfidence and excess volatility in general equilibrium," Econometric Society 2004 Latin American Meetings 157, Econometric Society. [Downloadable!]
  5. Silvia Goncalves & Massimo Guidolin, 2005. "Predictable dynamics in the S&P 500 index options implied volatility surface," Working Papers 2005-010, Federal Reserve Bank of St. Louis. [Downloadable!]
    Other versions:
  6. Massimo Guidolin, 2005. "High equity premia and crash fears. Rational foundations," Working Papers 2005-011, Federal Reserve Bank of St. Louis. [Downloadable!]
    Other versions:
  7. Massimo Guidolin, 2005. "Pessimistic beliefs under rational learning: quantitative implications for the equity premium puzzle," Working Papers 2005-005, Federal Reserve Bank of St. Louis. [Downloadable!]
    Other versions:
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