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

Author

Listed:
  • Elena-Ivona Dumitrescu

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

  • Christophe Hurlin

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

  • Vinson Pham

    (UCSC - University of California [Santa Cruz])

Abstract

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.

Suggested Citation

  • Elena-Ivona Dumitrescu & Christophe Hurlin & Vinson Pham, 2012. "Backtesting Value-at-Risk: From Dynamic Quantile to Dynamic Binary Tests," Working Papers halshs-00671658, HAL.
  • Handle: RePEc:hal:wpaper:halshs-00671658
    Note: View the original document on HAL open archive server: https://halshs.archives-ouvertes.fr/halshs-00671658
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    References listed on IDEAS

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    1. Christophe Pérignon & R.D. Smith, 2008. "A New Approach to Comparing VaR Estimation Methods," Post-Print hal-00854087, HAL.
    2. Bertrand Candelon & Gilbert Colletaz & Christophe Hurlin & Sessi Tokpavi, 2011. "Backtesting Value-at-Risk: A GMM Duration-Based Test," Journal of Financial Econometrics, Society for Financial Econometrics, vol. 9(2), pages 314-343, Spring.
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    1. repec:eee:eneeco:v:66:y:2017:i:c:p:523-534 is not listed on IDEAS
    2. Benjamin R. Auer & Benjamin Mögel, 2016. "How Accurate are Modern Value-at-Risk Estimators Derived from Extreme Value Theory?," CESifo Working Paper Series 6288, CESifo Group Munich.
    3. Wied, Dominik & Weiß, Gregor N.F. & Ziggel, Daniel, 2016. "Evaluating Value-at-Risk forecasts: A new set of multivariate backtests," Journal of Banking & Finance, Elsevier, vol. 72(C), pages 121-132.
    4. Boucher, Christophe M. & Daníelsson, Jón & Kouontchou, Patrick S. & Maillet, Bertrand B., 2014. "Risk models-at-risk," Journal of Banking & Finance, Elsevier, vol. 44(C), pages 72-92.
    5. Manuela Braione & Nicolas K. Scholtes, 2016. "Forecasting Value-at-Risk under Different Distributional Assumptions," Econometrics, MDPI, Open Access Journal, vol. 4(1), pages 1-27, January.
    6. Ziggel, Daniel & Berens, Tobias & Weiß, Gregor N.F. & Wied, Dominik, 2014. "A new set of improved Value-at-Risk backtests," Journal of Banking & Finance, Elsevier, vol. 48(C), pages 29-41.
    7. Michael B. Gordy & Alexander J. McNeil, 2017. "Spectral backtests of forecast distributions with application to risk management," Papers 1708.01489, arXiv.org, revised Mar 2018.
    8. Rachida Hennani, 2015. "Can the Lasota(1977)’s model compete with the Mackey-Glass(1977)’s model in nonlinear modelling of financial time series?," Working Papers 15-09, LAMETA, Universtiy of Montpellier, revised Jun 2015.
    9. Ana-Maria Fuertes & Jose Olmo, 2016. "On Setting Day-Ahead Equity Trading Risk Limits: VaR Prediction at Market Close or Open?," Journal of Risk and Financial Management, MDPI, Open Access Journal, vol. 9(3), pages 1-20, September.
    10. repec:dau:papers:123456789/15232 is not listed on IDEAS

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    Keywords

    Value-at-Risk; Risk Management; Dynamic Binary Choice Models;

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