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Bayesian Estimation of a Stochastic Volatility Model Using Option and Spot Prices: Application of a Bivariate Kalman Filter

Author

Listed:
  • Catherine S. Forbes
  • Gael M. Martin
  • Jill Wright

Abstract

In this paper Bayesian methods are applied to a stochastic volatility model using both the prices of the asset and the prices of options written on the asset. Posterior densities for all model parameters, latent volatilities and the market price of volatility risk are produced via a hybrid Markov Chain Monte Carlo sampling algorithm. Candidate draws for the unobserved volatilities are obtained by applying the Kalman filter and smoother to a linearization of a state-space representation of the model. The method is illustrated using the Heston (1993) stochastic volatility model applied to Australian News Corporation spot and option price data. Alternative models nested in the Heston framework are ranked via Bayes Factors and via fit, predictive and hedging performance.

Suggested Citation

  • Catherine S. Forbes & Gael M. Martin & Jill Wright, 2003. "Bayesian Estimation of a Stochastic Volatility Model Using Option and Spot Prices: Application of a Bivariate Kalman Filter," Monash Econometrics and Business Statistics Working Papers 17/03, Monash University, Department of Econometrics and Business Statistics.
    • Handle: RePEc:msh:ebswps:2003-17
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    File URL: http://www.buseco.monash.edu.au/ebs/pubs/wpapers/2003/wp17-03.pdf
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    Cited by:

    1. 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.
    2. Hanno Gottschalk & Elpida Nizami & Marius Schubert, 2016. "Option Pricing in Markets with Unknown Stochastic Dynamics," Papers 1602.04848, arXiv.org, revised Jan 2017.

    More about this item

    Keywords

    Option Pricing; Volatility Risk; Markov Chain Monte Carlo; Nonlinear State Space Model; Kalman Filter and Smoother.;
    All these keywords.

    JEL classification:

    • C11 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Bayesian Analysis: General
    • G13 - Financial Economics - - General Financial Markets - - - Contingent Pricing; Futures Pricing

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