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Bayesian parameter inference for models of the Black and Scholes type

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  • Henryk Gzyl
  • Enrique ter Horst
  • Samuel W. Malone

Abstract

In this paper, we describe a general method for constructing the posterior distribution of the mean and volatility of the return of an asset satisfying dS=SdX for some simple models of X. Our framework takes as inputs the prior distributions of the parameters of the stochastic process followed by the underlying, as well as the likelihood function implied by the observed price history for the underlying. As an application of our framework, we compute the value at risk (VaR) and conditional VaR (CVaR) measures for the changes in the price of an option implied by the posterior distribution of the volatility of the underlying. The implied VaR and CVaR are more conservative than their classical counterpart, since it takes into account the estimation risk that arises due to parameter uncertainty. Copyright © 2008 John Wiley & Sons, Ltd.

Suggested Citation

  • Henryk Gzyl & Enrique ter Horst & Samuel W. Malone, 2008. "Bayesian parameter inference for models of the Black and Scholes type," Applied Stochastic Models in Business and Industry, John Wiley & Sons, vol. 24(6), pages 507-524, November.
    • Handle: RePEc:wly:apsmbi:v:24:y:2008:i:6:p:507-524
    DOI: 10.1002/asmb.709
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    References listed on IDEAS

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    1. Karolyi, G. Andrew, 1993. "A Bayesian Approach to Modeling Stock Return Volatility for Option Valuation," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 28(4), pages 579-594, December.
    2. Darsinos, T. & Satchell, S.E., 2001. "Bayesian Analysis of the Black-Scholes Option Price," Cambridge Working Papers in Economics 0102, Faculty of Economics, University of Cambridge.
    3. Wang, Shaun S. & Young, Virginia R. & Panjer, Harry H., 1997. "Axiomatic characterization of insurance prices," Insurance: Mathematics and Economics, Elsevier, vol. 21(2), pages 173-183, November.
    4. Robert R. Bliss & Nikolaos Panigirtzoglou, 2004. "Option-Implied Risk Aversion Estimates," Journal of Finance, American Finance Association, vol. 59(1), pages 407-446, February.
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