Backtesting Parametric Value-at-Risk With Estimation Risk
AbstractOne 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 InfoArticle provided by American Statistical Association in its journal Journal of Business and Economic Statistics.
Volume (Year): 28 (2010)
Issue (Month): 1 ()
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- 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.
- C52 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Evaluation, Validation, and Selection
- C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models
- G21 - Financial Economics - - Financial Institutions and Services - - - Banks; Other Depository Institutions; Micro Finance Institutions; Mortgages
- G32 - Financial Economics - - Corporate Finance and Governance - - - Financing Policy; Financial Risk and Risk Management; Capital and Ownership Structure; Value of Firms; Goodwill
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
- Jianqing Fan & Juan Gu, 2003. "Semiparametric estimation of Value at Risk," Econometrics Journal, Royal Economic Society, vol. 6(2), pages 261-290, December.
- Steven N. Durlauf, 1992.
"Spectral Based Testing of the Martingale Hypothesis,"
NBER Technical Working Papers
0090, National Bureau of Economic Research, Inc.
- Durlauf, Steven N., 1991. "Spectral based testing of the martingale hypothesis," Journal of Econometrics, Elsevier, vol. 50(3), pages 355-376, December.
- Giacomini, Raffaella & Komunjer, Ivana, 2005.
"Evaluation and Combination of Conditional Quantile Forecasts,"
Journal of Business & Economic Statistics,
American Statistical Association, vol. 23, pages 416-431, October.
- Raffaella Giacomini & Ivana Komunjer, 2003. "Evaluation and Combination of Conditional Quantile Forecasts," Boston College Working Papers in Economics 571, Boston College Department of Economics.
- 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.
- Martins-Filho Carlos & Yao Feng, 2006. "Estimation of Value-at-Risk and Expected Shortfall based on Nonlinear Models of Return Dynamics and Extreme Value Theory," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 10(2), pages 1-43, May.
- Carlos Escanciano, J., 2008. "Joint and marginal specification tests for conditional mean and variance models," Journal of Econometrics, Elsevier, vol. 143(1), pages 74-87, March.
- Keith Kuester & Stefan Mittnik & Marc S. Paolella, 2006. "Value-at-Risk Prediction: A Comparison of Alternative Strategies," Journal of Financial Econometrics, Society for Financial Econometrics, vol. 4(1), pages 53-89.
- 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.
- Valentina Corradi & Norman R. Swanson, 2007.
"Nonparametric Bootstrap Procedures For Predictive Inference Based On Recursive Estimation Schemes,"
International Economic Review,
Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 48(1), pages 67-109, 02.
- Norman Swanson & Valentina Corradi, 2006. "Nonparametric Bootstrap Procedures for Predictive Inference Based on Recursive Estimation Schemes," Departmental Working Papers 200618, Rutgers University, Department of Economics.
- Oliver Linton & Yoon-Jae Whang, 2004.
"A Quantilogram Approach to Evaluating Directional Predictability,"
Cowles Foundation Discussion Papers
1454, Cowles Foundation for Research in Economics, Yale University.
- Oliver Linton & Yoon-Jae Whang, 2003. "A Quantilogram Approach to Evaluating Directional Predictability," STICERD - Econometrics Paper Series /2003/463, Suntory and Toyota International Centres for Economics and Related Disciplines, LSE.
- repec:cup:cbooks:9780521496032 is not listed on IDEAS
- Joan Jasiak & C. Gourieroux, 2006.
"Dynamic Quantile Models,"
2006_4, York University, Department of Economics.
- Li, W K & Ling, Shiqing & McAleer, Michael, 2002. " Recent Theoretical Results for Time Series Models with GARCH Errors," Journal of Economic Surveys, Wiley Blackwell, vol. 16(3), pages 245-69, July.
- Delgado, Miguel A. & Escanciano, Juan Carlos, 2007.
"Nonparametric Tests for Conditional Symmetry in Dynamic Models,"
Open Access publications from Universidad Carlos III de Madrid
info:hdl:10016/2494, Universidad Carlos III de Madrid.
- 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.
- 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.
- Peter Christoffersen & Jinyong Hahn & Atsushi Inoue, 2001.
"Testing and Comparing Value-at-Risk Measures,"
CIRANO Working Papers
- Mc Cracken, Michael W., 2000. "Robust out-of-sample inference," Journal of Econometrics, Elsevier, vol. 99(2), pages 195-223, December.
- Qi Li & Jeffrey Scott Racine, 2006. "Nonparametric Econometrics: Theory and Practice," Economics Books, Princeton University Press, edition 1, volume 1, number 8355, May.
- Koenker, Roger & Zhao, Quanshui, 1996. "Conditional Quantile Estimation and Inference for Arch Models," Econometric Theory, Cambridge University Press, vol. 12(05), pages 793-813, December.
- Sylvain Benoit & Christophe Hurlin & Christophe Pérignon, 2013. "Implied Risk Exposures," Working Papers halshs-00836280, HAL.
- 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.
- Christophe Hurlin & Gilbert Colletaz & Sessi Tokpavi & Bertrand Candelon, 2008.
"Backtesting Value-at-Risk: A GMM Duration-Based Test,"
- 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.
- Candelon Bertrand & Colletaz Gilberg & Hurlin Christophe & Tokpavi Sessi, 2009. "Backtesting Value-at-Risk: A GMM Duration-based Test," Research Memoranda 051, Maastricht : METEOR, Maastricht Research School of Economics of Technology and Organization.
- Gourieroux, Christian & Zakoïan, Jean-Michel, 2013.
Cambridge University Press, vol. 29(04), pages 735-770, August.
- Juan Carlos Escanciano & Pei Pei, 2012.
"Pitfalls in Backtesting Historical Simulation VaR Models,"
Caepr Working Papers
2012-003, Center for Applied Economics and Policy Research, Economics Department, Indiana University Bloomington.
- Escanciano, Juan Carlos & Pei, Pei, 2012. "Pitfalls in backtesting Historical Simulation VaR models," Journal of Banking & Finance, Elsevier, vol. 36(8), pages 2233-2244.
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