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Bayesian Estimation of a Stochastic Volatility Model Using Option and Spot Prices

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Author Info
C.S. Forbes ()
G.M. Martin ()
J. Wright

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Abstract

In this paper we apply Bayesian methods to estimate a stochastic volatility model using both the prices of the asset and the prices of options written on the asset. Implicit posterior densities for the parameters of the volatility model, for the latent volatilities and for the market price of volatility risk are produced. The method involves augmenting the data generating process associated with a panel of option prices with the probability density function describing the dynamics of the underlying bivariate spot price and volatility process. Posterior results are produced via a hybrid Markov Chain Monte Carlo sampling algorithm. Candidate draws which assume a given dynamic process for the volatility are re-weighted according to the information in both the option and spot price data. The method is illustrated using the Heston (1993) stochastic volatility model, based on data simulated to mimic the features of recent S&P500 spot and option price data. The way in which alternative option pricing models can be ranked, via Bayes Factors and via fit, predictive and hedging performance, is demonstrated.

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Paper provided by Monash University, Department of Econometrics and Business Statistics in its series Monash Econometrics and Business Statistics Working Papers with number 2/02.

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Length: 40 pages
Date of creation: Feb 2002
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Handle: RePEc:msh:ebswps:2002-2

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Related research
Keywords: Option Pricing Stochastic Volatility Volatility Risk Bayesian Implicit Inference Markov Chain Monte Carlo

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Find related papers by JEL classification:
C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: General - - - Estimation
C51 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Construction and Estimation
C52 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Evaluation and Testing
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. Gael Martin, 2001. "Bayesian Analysis Of A Fractional Cointegration Model," Econometric Reviews, Taylor and Francis Journals, vol. 20(2), pages 217-234. [Downloadable!] (restricted)
  2. Bates, David S, 1996. "Jumps and Stochastic Volatility: Exchange Rate Processes Implicit in Deutsche Mark Options," Review of Financial Studies, Oxford University Press for Society for Financial Studies, vol. 9(1), pages 69-107. [Downloadable!] (restricted)
  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. Yuri Kifer, 2000. "Game options," Finance and Stochastics, Springer, vol. 4(4), pages 443-463. [Downloadable!] (restricted)
  5. Cox, John C & Ingersoll, Jonathan E, Jr & Ross, Stephen A, 1985. "A Theory of the Term Structure of Interest Rates," Econometrica, Econometric Society, vol. 53(2), pages 385-407, March. [Downloadable!] (restricted)
  6. Kleibergen, F.R. & Van Dijk, H.K., 1993. "On the Shape of the Likelyhood/Posterior in Cointegration Models," Papers 9315-a, Erasmus University of Rotterdam - Econometric Institute.
  7. Gael M. Martin & Catherine S. Forbes & Vance L. Martin, 2003. "Implicit Bayesian Inference Using Option Prices," Monash Econometrics and Business Statistics Working Papers 5/03, Monash University, Department of Econometrics and Business Statistics. [Downloadable!]
    Other versions:
  8. Guo, Dajiang, 1998. "The Risk Premium of Volatility Implicit in Currency Options," Journal of Business & Economic Statistics, American Statistical Association, vol. 16(4), pages 498-507, October.
  9. 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)
  10. Martin, G.M., 1998. "U.S. Deficit Sustainability: A New Approach Based on Multiple Endogenous Breaks," Monash Econometrics and Business Statistics Working Papers 1/98, Monash University, Department of Econometrics and Business Statistics.
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  11. Pan, Jun, 2002. "The jump-risk premia implicit in options: evidence from an integrated time-series study," Journal of Financial Economics, Elsevier, vol. 63(1), pages 3-50, January. [Downloadable!] (restricted)
  12. 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)
  13. repec:cup:etheor:v:12:y:1996:i:3:p:409-31 is not listed on IDEAS
  14. Eraker, Bjorn, 2002. "Do Stock Prices and Volatility Jump? Reconciling Evidence from Spot and Option Prices," Working Papers 02-23, Duke University, Department of Economics. [Downloadable!]
  15. Koop, Gary & Potter, Simon M., 1998. "Bayes factors and nonlinearity: Evidence from economic time series1," Journal of Econometrics, Elsevier, vol. 88(2), pages 251-281, November. [Downloadable!] (restricted)
  16. Chao, J. C. & Phillips, P. C. B., 1998. "Posterior distributions in limited information analysis of the simultaneous equations model using the Jeffreys prior," Journal of Econometrics, Elsevier, vol. 87(1), pages 49-86, August. [Downloadable!] (restricted)
  17. Bates, David S., 2000. "Post-'87 crash fears in the S&P 500 futures option market," Journal of Econometrics, Elsevier, vol. 94(1-2), pages 181-238. [Downloadable!] (restricted)
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. Nunzio Cappuccio & Diego Lubian & Davide Raggi, 2004. "MCMC Bayesian Estimation of a Skew-GED Stochastic Volatility Model," Studies in Nonlinear Dynamics & Econometrics, Berkeley Electronic Press, vol. 8(2), pages 1211-1211. [Downloadable!] (restricted)
    Other versions:
  2. Gael M. Martin & Catherine S. Forbes & Vance L. Martin, 2003. "Implicit Bayesian Inference Using Option Prices," Monash Econometrics and Business Statistics Working Papers 5/03, Monash University, Department of Econometrics and Business Statistics. [Downloadable!]
    Other versions:
  3. Nunzio Cappuccio & Diego Lubian & Davide Raggi, 2006. "Investigating asymmetry in US stock market indexes: evidence from a stochastic volatility model," Applied Financial Economics, Taylor and Francis Journals, vol. 16(6), pages 479-490, March. [Downloadable!] (restricted)
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