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Backtesting Value-at-Risk : A GMM Duration-based Test

Author

Listed:
  • Gilbert Colletaz

    (LEO - Laboratoire d'économie d'Orleans [2008-2011] - UO - Université d'Orléans - CNRS - Centre National de la Recherche Scientifique)

  • Christophe Hurlin

    (LEO - Laboratoire d'économie d'Orleans [2008-2011] - UO - Université d'Orléans - CNRS - Centre National de la Recherche Scientifique)

  • Sessi Tokpavi

    (LEO - Laboratoire d'économie d'Orleans [2008-2011] - UO - Université d'Orléans - CNRS - Centre National de la Recherche Scientifique)

Abstract

This paper proposes a new duration-based backtesting procedure for VaR forecasts. The GMM test framework proposed by Bontemps (2006) to test for the distributional assumption (i.e. the geometric distribution) is applied to the case of the VaR forecasts validity. Using simple J-statistic based on the moments defined by the orthonormal polynomials associated with the geometric distribution, this new approach tackles most of the drawbacks usually associated to duration based backtesting procedures. First, its implementation is extremely easy. Second, it allows for a separate test for unconditional coverage, independence and conditional coverage hypothesis (Christoffersen, 1998). Third, feasibility of the tests is improved. Fourth, Monte-Carlo simulations show that for realistic sample sizes, our GMM test outperforms traditional duration based test. An empirical application for Nasdaq returns confirms that using GMM test leads to major consequences for the ex-post evaluation of the risk by regulation authorities. Without any doubt, this paper provides a strong support for the empirical application of duration-based tests for VaR forecasts.
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Suggested Citation

  • Gilbert Colletaz & Christophe Hurlin & Sessi Tokpavi, 2008. "Backtesting Value-at-Risk : A GMM Duration-based Test," Post-Print halshs-00363165, HAL.
    • Handle: RePEc:hal:journl:halshs-00363165
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    JEL classification:

    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes
    • C52 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Evaluation, Validation, and Selection
    • G28 - Financial Economics - - Financial Institutions and Services - - - Government Policy and Regulation

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