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

Christophe Hurlin, Gilbert Colletaz, Sessi Tokpavi () and Bertrand Candelon
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Gilbert Colletaz: LEO - Laboratoire d'économie d'Orleans [2008-2011] - UO - Université d'Orléans - CNRS - Centre National de la Recherche Scientifique

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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.

Keywords: Value-at-Risk; backtesting; GMM; duration-based test (search for similar items in EconPapers)
Date: 2008-10-10
Note: View the original document on HAL open archive server: https://shs.hal.science/halshs-00329495
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Citations: View citations in EconPapers (12)

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Related works:
Journal Article: Backtesting Value-at-Risk: A GMM Duration-Based Test (2011)
Working Paper: Backtesting Value-at-Risk: A GMM Duration-Based Test (2009)
Working Paper: Backtesting Value-at-Risk: A GMM Duration-based Test (2008)
Working Paper: Backtesting Value-at-Risk: A GMM Duration-based Test (2008)
Working Paper: Backtesting Value-at-Risk: A GMM Duration-based Test (2008)
Working Paper: Backtesting Value-at-Risk: A GMM Duration-Based Test (2008)
Working Paper: Backtesting Value-at-Risk: A GMM Duration-Based-Test (2008)
Working Paper: Backtesting Value-at-Risk: A GMM Duration-Based Test (2008)
Working Paper: Backtesting Value-at-Risk: A GMM Duration-Based Test (2008)
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