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Bayesian Extreme Value Mixture Modelling for Estimating VaR

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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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  • Xin Zhao & Carl John Scarrott & Marco Reale & Les Oxley, 2009. "Bayesian Extreme Value Mixture Modelling for Estimating VaR," Working Papers in Economics 09/15, University of Canterbury, Department of Economics and Finance.
    • Handle: RePEc:cbt:econwp:09/15
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    File URL: https://repec.canterbury.ac.nz/cbt/econwp/0915.pdf
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    References listed on IDEAS

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    1. 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.
    2. 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.
    3. 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.
    4. 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.
    5. 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, May.
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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, Russian Presidential Academy of National Economy and Public Administration (RANEPA), vol. 27(3), pages 20-35.
    2. C J Scarrott & A MacDonald, 2010. "Extreme-value-model-based risk assessment for nuclear reactors," Journal of Risk and Reliability, , vol. 224(4), pages 239-252, December.

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    More about this item

    Keywords

    Extreme values; Bayesian; Threshold estimation; Value-at-Risk;
    All these keywords.

    JEL classification:

    • C11 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Bayesian Analysis: General
    • G12 - Financial Economics - - General Financial Markets - - - Asset Pricing; Trading Volume; Bond Interest Rates
    • G17 - Financial Economics - - General Financial Markets - - - Financial Forecasting and Simulation

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