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Backtesting Parametric Value-at-Risk With Estimation Risk

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  • Escanciano, J. Carlos
  • Olmo, Jose

Abstract

One of the implications of the creation of Basel Committee on Banking Supervision was the implementation of Value-at-Risk (VaR) as the standard tool for measuring market risk. Since then, the capital requirements of commercial banks with trading activities are based on VaR estimates. Therefore, appropriately constructed tests for assessing the out-of-sample forecast accuracy of the VaR model (backtesting procedures) have become of crucial practical importance. In this paper we show that the use of the standard unconditional and independence backtesting procedures to assess VaR models in out-of-sample composite environments can be misleading. These tests do not consider the impact of estimation risk and therefore may use wrong critical values to assess market risk. The purpose of this paper is to quantify such estimation risk in a very general class of dynamic parametric VaR models and to correct standard backtesting procedures to provide valid inference in out-of-sample analyses. A Monte Carlo study illustrates our theoretical findings in finite-samples and shows that our corrected unconditional test can provide more accurately sized and more powerful tests than the uncorrected one. Finally, an application to S&P500 Index shows the importance of this correction and its impact on capital requirements as imposed by Basel Accord.

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Bibliographic Info

Article provided by American Statistical Association in its journal Journal of Business and Economic Statistics.

Volume (Year): 28 (2010)
Issue (Month): 1 ()
Pages: 36-51

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Handle: RePEc:bes:jnlbes:v:28:i:1:y:2010:p:36-51

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  1. Giacomini, Raffaella & Komunjer, Ivana, 2002. "Evaluation and Combination of Conditional Quantile Forecasts," University of California at San Diego, Economics Working Paper Series qt4n99t4wz, Department of Economics, UC San Diego.
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  7. Delgado, Miguel A. & Carlos Escanciano, J., 2007. "Nonparametric tests for conditional symmetry in dynamic models," Journal of Econometrics, Elsevier, vol. 141(2), pages 652-682, December.
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  12. Escanciano, J. C. & Olmo, J., 2007. "Estimation risk effects on backtesting for parametric value-at-risk models," Working Papers 07/11, Department of Economics, City University London.
  13. Qi Li & Jeffrey Scott Racine, 2006. "Nonparametric Econometrics: Theory and Practice," Economics Books, Princeton University Press, edition 1, volume 1, number 8355.
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  17. Mc Cracken, Michael W., 2000. "Robust out-of-sample inference," Journal of Econometrics, Elsevier, vol. 99(2), pages 195-223, December.
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Cited by:
  1. Syed Adeel Hussain, 2013. "Differentiation of Market Risk Characteristics among Sharia Compliant and Conventional Equities listed on the Pakistani Capital Market - KSE 100 Index over a selective time period," 2013 Papers phu395, Job Market Papers.
  2. Christian Gouriéroux & Jean-Michel Zakoian, 2012. "Estimation Adjusted VaR," Working Papers 2012-16, Centre de Recherche en Economie et Statistique.
  3. Escanciano, Juan Carlos & Pei, Pei, 2012. "Pitfalls in backtesting Historical Simulation VaR models," Journal of Banking & Finance, Elsevier, vol. 36(8), pages 2233-2244.
  4. Evers, Corinna & Rohde, Johannes, 2014. "Model Risk in Backtesting Risk Measures," Hannover Economic Papers (HEP) dp-529, Leibniz Universität Hannover, Wirtschaftswissenschaftliche Fakultät.
  5. Sylvain Benoit & Christophe Hurlin & Christophe Pérignon, 2013. "Implied Risk Exposures," Working Papers halshs-00836280, HAL.
  6. Lönnbark, Carl, 2013. "On the role of the estimation error in prediction of expected shortfall," Journal of Banking & Finance, Elsevier, vol. 37(3), pages 847-853.
  7. Elena-Ivona Dumitrescu & Christophe Hurlin & Vinson Pham, 2012. "Backtesting Value-at-Risk: From Dynamic Quantile to Dynamic Binary Tests," Working Papers halshs-00671658, HAL.

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