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Backtesting Value-at-Risk: From Dynamic Quantile to Dynamic Binary Tests

  • Elena-Ivona Dumitrescu

    ()

    (LEO - Laboratoire d'économie d'Orleans - CNRS - UO - Université d'Orléans)

  • Christophe Hurlin

    ()

    (LEO - Laboratoire d'économie d'Orleans - CNRS - UO - Université d'Orléans)

  • Vinson Pham

    (UCSC - University of California at Santa Cruz - UNIVERSITY OF CALIFORNIA AT SANTA CRUZ)

In this paper we propose a new tool for backtesting that examines the quality of Value-at- Risk (VaR) forecasts. To date, the most distinguished regression-based backtest, proposed by Engle and Manganelli (2004), relies on a linear model. However, in view of the di- chotomic character of the series of violations, a non-linear model seems more appropriate. In this paper we thus propose a new tool for backtesting (denoted DB) based on a dy- namic binary regression model. Our discrete-choice model, e.g. Probit, Logit, links the sequence of violations to a set of explanatory variables including the lagged VaR and the lagged violations in particular. It allows us to separately test the unconditional coverage, the independence and the conditional coverage hypotheses and it is easy to implement. Monte-Carlo experiments show that the DB test exhibits good small sample properties in realistic sample settings (5% coverage rate with estimation risk). An application on a portfolio composed of three assets included in the CAC40 market index is nally proposed.

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Date of creation: 07 Feb 2012
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Handle: RePEc:hal:wpaper:halshs-00671658
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  1. Gilbert COLLETAZ & Christophe HURLIN & Sessi TOKPAVI, 2009. "Backtesting Value-at-Risk: A GMM Duration-Based Test," LEO Working Papers / DR LEO 265, Orleans Economics Laboratory / Laboratoire d'Economie d'Orleans (LEO), University of Orleans.
  2. DUFOUR, Jean-Marie, 2005. "Monte Carlo Tests with Nuisance Parameters: A General Approach to Finite-Sample Inference and Nonstandard Asymptotics," Cahiers de recherche 03-2005, Centre interuniversitaire de recherche en économie quantitative, CIREQ.
  3. Jeremy Berkowitz & James O'Brien, 2002. "How Accurate Are Value-at-Risk Models at Commercial Banks?," Journal of Finance, American Finance Association, vol. 57(3), pages 1093-1111, 06.
  4. Jeremy Berkowitz & Peter Christoffersen & Denis Pelletier, 2011. "Evaluating Value-at-Risk Models with Desk-Level Data," Management Science, INFORMS, vol. 57(12), pages 2213-2227, December.
  5. Peter Christoffersen & Denis Pelletier, 2003. "Backtesting Value-at-Risk: A Duration-Based Approach," CIRANO Working Papers 2003s-05, CIRANO.
  6. Gaglianone, Wagner Piazza & Linton, Oliver & Lima, Luiz Renato Regis de Oliveira, 2008. "Evaluating Value-at-Risk models via Quantile regressions," Economics Working Papers (Ensaios Economicos da EPGE) 679, FGV/EPGE Escola Brasileira de Economia e Finanças, Getulio Vargas Foundation (Brazil).
  7. Gouriéroux, Christian & Laurent, J.P. & Scaillet, Olivier, 1999. "Sensitivity Analysis of Values at Risk," Discussion Papers (IRES - Institut de Recherches Economiques et Sociales) 2000002, Université catholique de Louvain, Institut de Recherches Economiques et Sociales (IRES), revised 00 Jan 2000.
  8. Christophe Hurlin & Sessi Tokpavi, 2007. "Un test de Validité de la Value-at-risk," Post-Print halshs-00272963, HAL.
  9. Christophe HURLIN & Sessi TOKPAVI, 2007. "Une évaluation des procédures de Backtesting," LEO Working Papers / DR LEO 1716, Orleans Economics Laboratory / Laboratoire d'Economie d'Orleans (LEO), University of Orleans.
  10. Robert Engle & Simone Manganelli, 2000. "CAViaR: Conditional Autoregressive Value at Risk by Regression Quantiles," Econometric Society World Congress 2000 Contributed Papers 0841, Econometric Society.
  11. Gourieroux,Christian, 2000. "Econometrics of Qualitative Dependent Variables," Cambridge Books, Cambridge University Press, number 9780521331494, june. pag.
  12. Gourieroux,Christian, 2000. "Econometrics of Qualitative Dependent Variables," Cambridge Books, Cambridge University Press, number 9780521589857, june. pag.
  13. Elisabetta Falcetti & Merxe Tudela, 2006. "Modelling Currency Crises in Emerging Markets: A Dynamic Probit Model with Unobserved Heterogeneity and Autocorrelated Errors," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 68(4), pages 445-471, 08.
  14. Heikki Kauppi & Pentti Saikkonen, 2008. "Predicting U.S. Recessions with Dynamic Binary Response Models," The Review of Economics and Statistics, MIT Press, vol. 90(4), pages 777-791, November.
  15. 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.).
  16. Christophe Pérignon & R.D. Smith, 2008. "A New Approach to Comparing VaR Estimation Methods," Post-Print hal-00854087, HAL.
  17. Juan Carlos Escanciano & Jose Olmo, 2007. "Backtesting Parametric Value-at-Risk with Estimation Risk," Caepr Working Papers 2007-005_updated, Center for Applied Economics and Policy Research, Economics Department, Indiana University Bloomington.
  18. Engle, Robert, 2002. "Dynamic Conditional Correlation: A Simple Class of Multivariate Generalized Autoregressive Conditional Heteroskedasticity Models," Journal of Business & Economic Statistics, American Statistical Association, vol. 20(3), pages 339-50, July.
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