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

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  • C.S. Forbes

    ()

  • G.M. Martin

    ()

  • J. Wright

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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File URL: http://www.buseco.monash.edu.au/ebs/pubs/wpapers/2002/wp2-02.pdf
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Bibliographic Info

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
Date of revision:
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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References

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  1. Siddhartha Chib & Edward Greenberg, 1994. "Markov Chain Monte Carlo Simulation Methods in Econometrics," Econometrics 9408001, EconWPA, revised 24 Oct 1994.
  2. 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.
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  13. Yuri Kifer, 2000. "Game options," Finance and Stochastics, Springer, vol. 4(4), pages 443-463.
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  15. Kleibergen, Frank & van Dijk, Herman K., 1994. "On the Shape of the Likelihood/Posterior in Cointegration Models," Econometric Theory, Cambridge University Press, vol. 10(3-4), pages 514-551, August.
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Cited by:
  1. Cappuccio Nunzio & Lubian Diego & Raggi Davide, 2004. "MCMC Bayesian Estimation of a Skew-GED Stochastic Volatility Model," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 8(2), pages 1-31, May.

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