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On Bayesian Value at Risk: From Linear to Non-Linear Portfolios

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Author Info

  • Tak Siu

    ()

  • Howell Tong

    ()

  • Hailiang Yang

    ()

Abstract

This paper proposes the use of Bayesian approach to implement Value at Risk (VaR) model for both linear and non-linear portfolios. The Bayesian approach provides risk traders with the flexibility of adjusting their VaR models according to their subjective views. First, we deal with the case of linear portfolios. By imposing the conjugate-prior assumptions, a closed-form expression for the Bayesian VaR is obtained. The Bayesian VaR model can also be adjusted in order to deal with the ageing effect of the past data. By adopting Gerber-Shiu's option-pricing model, our Bayesian VaR model can also be applied to deal with non-linear portfolios of derivatives. We obtain an exact formula for the Bayesian VaR in the case of a single European call option. We adopt the method of back-testing to compare the non-adjusted and adjusted Bayesian VaR models with their corresponding classical counterparts in both linear and non-linear cases. Copyright Springer Science+Business Media, Inc. 2004

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File URL: http://hdl.handle.net/10.1007/s10690-006-9008-7
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Bibliographic Info

Article provided by Springer in its journal Asia-Pacific Financial Markets.

Volume (Year): 11 (2004)
Issue (Month): 2 (June)
Pages: 161-184

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Handle: RePEc:kap:apfinm:v:11:y:2004:i:2:p:161-184

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Web page: http://springerlink.metapress.com/link.asp?id=102851

Related research

Keywords: subjective VaR; Bayesian method; Gerber-Shiu's model; leptokurtic effect; non-linear portfolios; model risk;

References

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  1. Hans FÃllmer & Peter Leukert, 1999. "Quantile hedging," Finance and Stochastics, Springer, vol. 3(3), pages 251-273.
  2. Tauchen, George E & Pitts, Mark, 1983. "The Price Variability-Volume Relationship on Speculative Markets," Econometrica, Econometric Society, vol. 51(2), pages 485-505, March.
  3. Ait-Sahalia, Yacine & Lo, Andrew W., 2000. "Nonparametric risk management and implied risk aversion," Journal of Econometrics, Elsevier, vol. 94(1-2), pages 9-51.
  4. Clark, Peter K, 1973. "A Subordinated Stochastic Process Model with Finite Variance for Speculative Prices," Econometrica, Econometric Society, vol. 41(1), pages 135-55, January.
  5. Ioannis Karatzas & Jaksa Cvitanic, 1999. "On dynamic measures of risk," Finance and Stochastics, Springer, vol. 3(4), pages 451-482.
  6. Wolfgang J. Runggaldier & Anna Zaccaria, 2000. "A Stochastic Control Approach to Risk Management Under Restricted Information," Mathematical Finance, Wiley Blackwell, vol. 10(2), pages 277-288.
  7. Philippe Artzner & Freddy Delbaen & Jean-Marc Eber & David Heath, 1999. "Coherent Measures of Risk," Mathematical Finance, Wiley Blackwell, vol. 9(3), pages 203-228.
  8. Brennan, M J, 1979. "The Pricing of Contingent Claims in Discrete Time Models," Journal of Finance, American Finance Association, vol. 34(1), pages 53-68, March.
  9. McNeil, Alexander J. & Frey, Rudiger, 2000. "Estimation of tail-related risk measures for heteroscedastic financial time series: an extreme value approach," Journal of Empirical Finance, Elsevier, vol. 7(3-4), pages 271-300, November.
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Citations

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Cited by:
  1. John Cotter & Kevin Dowd, 2011. "Evaluating the Precision of Estimators of Quantile-Based Risk Measures," Working Papers 200743, Geary Institute, University College Dublin.
  2. Carol Alexandra, 2003. "The Present, Future and Imperfect of Financial Risk Management," ICMA Centre Discussion Papers in Finance icma-dp2003-12, Henley Business School, Reading University, revised Feb 2004.

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