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Bayesian Extreme Value Mixture Modelling for Estimating VaR

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Author Info

  • Xin Zhao
  • Carl John Scarrott
  • Marco Reale
  • Les Oxley

    ()
    (University of Canterbury)

Abstract

A new extreme value mixture modelling approach for estimating Value-at-Risk (VaR) is proposed, overcoming the key issues of determining the threshold which defines the distribution tail and accounts for uncertainty due to threshold choice. A two-stage approach is adopted: volatility estimation followed by conditional extremal modelling of the independent innovations. Bayesian inference is used to account for all uncertainties and enables inclusion of expert prior information, potentially overcoming the inherent sparsity of extremal data. Simulations show the reliability and flexibility of the proposed mixture model, followed by VaR forecasting for capturing returns during the current financial crisis.

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File URL: http://www.econ.canterbury.ac.nz/RePEc/cbt/econwp/0915.pdf
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Bibliographic Info

Paper provided by University of Canterbury, Department of Economics and Finance in its series Working Papers in Economics with number 09/15.

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Length: 34 pages
Date of creation: 27 Oct 2009
Date of revision:
Handle: RePEc:cbt:econwp:09/15

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Related research

Keywords: Extreme values; Bayesian; Threshold estimation; Value-at-Risk;

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References

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  1. Christopher A. T. Ferro & Johan Segers, 2003. "Inference for clusters of extreme values," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 65(2), pages 545-556.
  2. Hang Chan, Ngai & Deng, Shi-Jie & Peng, Liang & Xia, Zhendong, 2007. "Interval estimation of value-at-risk based on GARCH models with heavy-tailed innovations," Journal of Econometrics, Elsevier, vol. 137(2), pages 556-576, April.
  3. Les Oxley & Marco Reale & Carl Scarrott & Xin Zhao, 2009. "Extreme Value GARCH modelling with Bayesian Inference," Working Papers in Economics 09/05, University of Canterbury, Department of Economics and Finance.
  4. Bali, Turan G. & Weinbaum, David, 2007. "A conditional extreme value volatility estimator based on high-frequency returns," Journal of Economic Dynamics and Control, Elsevier, vol. 31(2), pages 361-397, February.
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Cited by:
  1. Shcherba, Alexandr, 2012. "Market risk valuation modeling for the European countries at the financial crisis of 2008," Applied Econometrics, Publishing House "SINERGIA PRESS", vol. 27(3), pages 20-35.

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