University of Paris Ouest, Nanterre
Sessi Tokpavi created these companion sites
Backtesting Value-at-Risk: A GMM Duration-based Test
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, Monte-Carlo simulations show that for realistic sample sizes, our GMM test outperforms traditional duration based test. Besides, we study the consequences of the estimation risk on the duration-based backtesting tests and propose a sub-sampling approach for robust inference derived from Escanciano and Olmo (2009). 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.
Last updateThu Jun 28 11:01:00 CEST 2012
Backtesting Value-at-Risk Accuracy: A Simple New Test
This paper proposes a new test of value-at-risk (VAR) validation. Our test exploits the idea that the sequence of VAR violations (hit function) – taking value 1 - α if there is a violation, and -α otherwise – for a nominal coverage rate α verifies the properties of a martingale difference if the model used to quantify risk is adequate (Berkowitz et al., 2005). More precisely, we use the multivariate portmanteau statistic of Li and McLeod (1981), an extension to the multivariate framework of the test of Box and Pierce (1970), to jointly test the absence of autocorrelation in the vector of hit sequences for various coverage rates considered relevant for the management of extreme risks. We show that this shift to a multivariate dimension appreciably improves the power properties of the VAR validation test for reasonable sample sizes.
Last updateTue Mar 13 05:03:00 CET 2012