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Predictive Performance of Conditional Extreme Value Theory and Conventional Methods in Value at Risk Estimation

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  • Ghorbel, Ahmed
  • Trabelsi, Abdelwahed

Abstract

This paper conducts a comparative evaluation of the predictive performance of various Value at Risk (VaR) models such as GARCH-normal, GARCH-t, EGARCH, TGARCH models, variance-covariance method, historical simulation and filtred Historical Simulation, EVT and conditional EVT methods. Special emphasis is paid on two methodologies related to the Extreme Value Theory (EVT): The Peaks over Threshold (POT) and the Block Maxima (BM). Both estimation techniques are based on limits results for the excess distribution over high thresholds and block maxima, respectively. We apply both unconditional and conditional EVT models to management of extreme market risks in stock markets. They are applied on daily returns of the Tunisian stock exchange (BVMT) and CAC 40 indexes with the intension to compare the performance of various estimation methods on markets with different capitalization and trading practices. The sample extends over the period July 29, 1994 to December 30, 2005. We use a rolling windows of approximately four years (n= 1000 days). The sub-period from July, 1998 for BVMT (from August 4, 1998 for CAC 40) has been reserved for backtesting purposes. The results we report demonstrate that conditional POT-EVT method produces the most accurate forecasts of extreme losses both for standard and more extreme VaR quantiles. The conditional block maxima EVT method is less accurate.

Suggested Citation

  • Ghorbel, Ahmed & Trabelsi, Abdelwahed, 2007. "Predictive Performance of Conditional Extreme Value Theory and Conventional Methods in Value at Risk Estimation," MPRA Paper 3963, University Library of Munich, Germany.
  • Handle: RePEc:pra:mprapa:3963
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    File URL: https://mpra.ub.uni-muenchen.de/3963/1/MPRA_paper_3963.pdf
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    References listed on IDEAS

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    1. Francis X. Diebold & Til Schuermann & John D. Stroughair, 1998. "Pitfalls and Opportunities in the Use of Extreme Value Theory in Risk Management," Center for Financial Institutions Working Papers 98-10, Wharton School Center for Financial Institutions, University of Pennsylvania.
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    3. Paul H. Kupiec, 1995. "Techniques for verifying the accuracy of risk measurement models," Finance and Economics Discussion Series 95-24, Board of Governors of the Federal Reserve System (U.S.).
    4. Torben G. Andersen & Tim Bollerslev & Peter Christoffersen & Francis X. Diebold, 2007. "Practical Volatility and Correlation Modeling for Financial Market Risk Management," NBER Chapters,in: The Risks of Financial Institutions, pages 513-548 National Bureau of Economic Research, Inc.
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    7. Ser-Huang Poon & Clive W.J. Granger, 2003. "Forecasting Volatility in Financial Markets: A Review," Journal of Economic Literature, American Economic Association, vol. 41(2), pages 478-539, June.
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    Cited by:

    1. Nguyen, Cuong C. & Bhatti, M. Ishaq, 2012. "Copula model dependency between oil prices and stock markets: Evidence from China and Vietnam," Journal of International Financial Markets, Institutions and Money, Elsevier, vol. 22(4), pages 758-773.
    2. Bhatti, M. Ishaq & Nguyen, Cuong C., 2012. "Diversification evidence from international equity markets using extreme values and stochastic copulas," Journal of International Financial Markets, Institutions and Money, Elsevier, vol. 22(3), pages 622-646.

    More about this item

    Keywords

    Financial Risk management; Value-at-Risk; Extreme Value Theory; Conditional EVT; Backtesting;

    JEL classification:

    • G0 - Financial Economics - - General
    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes
    • G15 - Financial Economics - - General Financial Markets - - - International Financial Markets

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