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

By Bertrand Candelon Y

Abstract

This paper 1 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 de…ned 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 (Christo¤ersen, 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 con…rms 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

Topics: J.E.L Classi…cation, C22, C52, G28
Year: 2008
OAI identifier: oai:CiteSeerX.psu:10.1.1.353.1367
Provided by: CiteSeerX
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