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Implicit Bayesian Inference Using Option Prices

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Author Info
Gael M. Martin ()
Catherine S. Forbes ()
Vance L. Martin

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Abstract

A Bayesian approach to option pricing is presented, in which posterior inference about the underlying returns process is conducted implicitly via observed option prices. A range of models allowing for conditional leptokurtosis, skewness and time-varying volatility in returns are considered, with posterior parameter distributions and model probabilities backed out from the option prices. Models are ranked according to several criteria, including out-of-sample fit, predictive and hedging performance. The methodology accommodates heteroscedasticity and autocorrelation in the option pricing errors, as well as regime shifts across contract groups. The method is applied to intraday option price data on the S&P500 stock index for 1995. Whilst the results provide support for models which accommodate leptokurtosis, no one model dominates according to all criteria considered.

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Publisher Info
Paper provided by Monash University, Department of Econometrics and Business Statistics in its series Monash Econometrics and Business Statistics Working Papers with number 5/03.

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Length: 36 pages
Date of creation: Feb 2003
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Handle: RePEc:msh:ebswps:2003-5

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Related research
Keywords: Bayesian Option Pricing; Leptokurtosis; Skewness; GARCH Option Pricing; Option Price Prediction; Hedging Errors.;

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Find related papers by JEL classification:
C11 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: General - - - Bayesian Analysis
C16 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: General - - - Econometric and Statistical Methods; Specific Distributions
G13 - Financial Economics - - General Financial Markets - - - Contingent Pricing; Futures Pricing

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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.:
  1. Bollerslev, Tim & Ole Mikkelsen, Hans, 1999. "Long-term equity anticipation securities and stock market volatility dynamics," Journal of Econometrics, Elsevier, vol. 92(1), pages 75-99, September. [Downloadable!] (restricted)
  2. Bauwens, Luc & Lubrano, Michel, 2002. "Bayesian option pricing using asymmetric GARCH models," Journal of Empirical Finance, Elsevier, vol. 9(3), pages 321-342, August. [Downloadable!] (restricted)
    Other versions:
  3. Hull, John C & White, Alan D, 1987. " The Pricing of Options on Assets with Stochastic Volatilities," Journal of Finance, American Finance Association, vol. 42(2), pages 281-300, June. [Downloadable!] (restricted)
  4. Boyle, Phelim P. & Ananthanarayanan, A. L., 1977. "The impact of variance estimation in option valuation models," Journal of Financial Economics, Elsevier, vol. 5(3), pages 375-387, December. [Downloadable!] (restricted)
  5. Jacquier, Eric & Jarrow, Robert, 2000. "Bayesian analysis of contingent claim model error," Journal of Econometrics, Elsevier, vol. 94(1-2), pages 145-180. [Downloadable!] (restricted)
  6. G.C. Lim & G.M. Martin & V.L. Martin, 2002. "Parametric Pricing of Higher Order Moments in S&P500 Options," Monash Econometrics and Business Statistics Working Papers 1/02, Monash University, Department of Econometrics and Business Statistics. [Downloadable!]
    Other versions:
  7. Heston, Steven L & Nandi, Saikat, 2000. "A Closed-Form GARCH Option Valuation Model," Review of Financial Studies, Oxford University Press for Society for Financial Studies, vol. 13(3), pages 585-625.
  8. Jarrow, Robert & Rudd, Andrew, 1982. "Approximate option valuation for arbitrary stochastic processes," Journal of Financial Economics, Elsevier, vol. 10(3), pages 347-369, November. [Downloadable!] (restricted)
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  11. G.C. Lim & G.M. Martin & V.L. Martin, 2002. "Pricing Currency Options in Tranquil Markets: Modelling Volatility Frowns," Monash Econometrics and Business Statistics Working Papers 4/02, Monash University, Department of Econometrics and Business Statistics. [Downloadable!]
  12. Bollerslev, Tim & Chou, Ray Y. & Kroner, Kenneth F., 1992. "ARCH modeling in finance : A review of the theory and empirical evidence," Journal of Econometrics, Elsevier, vol. 52(1-2), pages 5-59. [Downloadable!] (restricted)
  13. Hafner, Christian M. & Herwartz, Helmut, 2001. "Option pricing under linear autoregressive dynamics, heteroskedasticity, and conditional leptokurtosis," Journal of Empirical Finance, Elsevier, vol. 8(1), pages 1-34, March. [Downloadable!] (restricted)
    Other versions:
  14. Chernov, Mikhail & Ghysels, Eric, 2000. "A study towards a unified approach to the joint estimation of objective and risk neutral measures for the purpose of options valuation," Journal of Financial Economics, Elsevier, vol. 56(3), pages 407-458, June. [Downloadable!] (restricted)
  15. Kabir K. Dutta & David F. Babbel, 2002. "Extracting Probabilistic Information from the Prices of Interest Rate Options: Tests of Distributional Assumptions," Center for Financial Institutions Working Papers 02-26, Wharton School Center for Financial Institutions, University of Pennsylvania. [Downloadable!]
    Other versions:
  16. 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)
  17. C.S. Forbes & G.M. Martin & J. Wright, 2002. "Bayesian Estimation of a Stochastic Volatility Model Using Option and Spot Prices," Monash Econometrics and Business Statistics Working Papers 2/02, Monash University, Department of Econometrics and Business Statistics. [Downloadable!]
  18. Bollerslev, Tim, 1986. "Generalized autoregressive conditional heteroskedasticity," Journal of Econometrics, Elsevier, vol. 31(3), pages 307-327, April. [Downloadable!] (restricted)
  19. Fernandez, C. & Steel, M.F.J., 1996. "On Bayesian modelling of fat tails and skewness," Discussion Paper 58, Tilburg University, Center for Economic Research. [Downloadable!]
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Full references

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. Anthony D. Hall & Paul Kofman & Steve Manaster, 2001. "Migration of Price Discovery With Constrained Futures Markets," Research Paper Series 70, Quantitative Finance Research Centre, University of Technology, Sydney. [Downloadable!]
  2. V. L. Martin & G. M. Martin & G. C. Lim, 2005. "Parametric pricing of higher order moments in S&P500 options," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 20(3), pages 377-404. [Downloadable!]
    Other versions:
  3. C.S. Forbes & G.M. Martin & J. Wright, 2002. "Bayesian Estimation of a Stochastic Volatility Model Using Option and Spot Prices," Monash Econometrics and Business Statistics Working Papers 2/02, Monash University, Department of Econometrics and Business Statistics. [Downloadable!]
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