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A review of backtesting and backtesting procedures

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  • Sean D. Campbell
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    Abstract

    This paper reviews a variety of backtests that examine the adequacy of Value-at-Risk (VaR) measures. These backtesting procedures are reviewed from both a statistical and risk management perspective. The properties of unconditional coverage and independence are defined and their relation to backtesting procedures is discussed. Backtests are then classified by whether they examine the unconditional coverage property, independence property, or both properties of a VaR measure. Backtests that examine the accuracy of a VaR model at several quantiles, rather than a single quantile, are also outlined and discussed. The statistical power properties of these tests are examined in a simulation experiment. Finally, backtests that are specified in terms of a pre-specified loss function are reviewed and their use in VaR validation is discussed.

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    Bibliographic Info

    Paper provided by Board of Governors of the Federal Reserve System (U.S.) in its series Finance and Economics Discussion Series with number 2005-21.

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    Date of creation: 2005
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    Handle: RePEc:fip:fedgfe:2005-21

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    Keywords: Risk management ; Bank investments;

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    1. Peter Christoffersen & Denis Pelletier, 2003. "Backtesting Value-at-Risk: A Duration-Based Approach," CIRANO Working Papers 2003s-05, CIRANO.
    2. Kerkhof, Jeroen & Melenberg, Bertrand, 2004. "Backtesting for risk-based regulatory capital," Journal of Banking & Finance, Elsevier, vol. 28(8), pages 1845-1865, August.
    3. Jose A. Lopez, 1997. "Regulatory evaluation of value-at-risk models," Staff Reports 33, Federal Reserve Bank of New York.
    4. Berkowitz, Jeremy, 2001. "Testing Density Forecasts, with Applications to Risk Management," Journal of Business & Economic Statistics, American Statistical Association, vol. 19(4), pages 465-74, October.
    5. Christoffersen, Peter F, 1998. "Evaluating Interval Forecasts," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 39(4), pages 841-62, November.
    6. Matthew Pritsker, 2001. "The hidden dangers of historical simulation," Finance and Economics Discussion Series 2001-27, Board of Governors of the Federal Reserve System (U.S.).
    7. Colleen Cassidy & Marianne Gizycki, 1997. "Measuring Traded Market Risk: Value-at-risk and Backtesting Techniques," RBA Research Discussion Papers rdp9708, Reserve Bank of Australia.
    8. Katerina Simons, 1996. "Value at risk: new approaches to risk management," New England Economic Review, Federal Reserve Bank of Boston, issue Sep, pages 3-13.
    9. 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.
    10. Diebold, Francis X & Gunther, Todd A & Tay, Anthony S, 1998. "Evaluating Density Forecasts with Applications to Financial Risk Management," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 39(4), pages 863-83, November.
    11. Matthew Pritsker, 1997. "Evaluating Value at Risk Methodologies: Accuracy versus Computational Time," Journal of Financial Services Research, Springer, vol. 12(2), pages 201-242, October.
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    Cited by:
    1. Wagner Piazza Gaglianone & Luiz Renato Lima & Oliver Linton & Daniel Smith, 2010. "Evaluating Value-at-Risk Models via Quantile Regression," NCER Working Paper Series 67, National Centre for Econometric Research.
    2. Evers, Corinna & Rohde, Johannes, 2014. "Model Risk in Backtesting Risk Measures," Hannover Economic Papers (HEP) dp-529, Leibniz Universität Hannover, Wirtschaftswissenschaftliche Fakultät.
    3. Christos Agiakloglou & Charalampos Agiropoulos, 2011. "The sensitivity of Value-at-Risk estimates using Monte Carlo approach," SPOUDAI Journal of Economics and Business, SPOUDAI Journal of Economics and Business, University of Piraeus, vol. 61(1-2), pages 7-12, January -.
    4. Jean-François Carpantier & Arnaud Dufays, 2013. "Commodities Inventory Effect," CREA Discussion Paper Series 13-07, Center for Research in Economic Analysis, University of Luxembourg.
    5. Sabrina Khanniche, 2009. "Evaluation of Hedge Fund Returns Value at Risk Using GARCH Models," EconomiX Working Papers 2009-46, University of Paris West - Nanterre la Défense, EconomiX.
    6. Escanciano, Juan Carlos & Pei, Pei, 2012. "Pitfalls in backtesting Historical Simulation VaR models," Journal of Banking & Finance, Elsevier, vol. 36(8), pages 2233-2244.
    7. Vêlayoudom Marimoutou & Bechir Raggad & Abdelwahed Trabelsi, 2006. "Extreme Value Theory and Value at Risk : Application to Oil Market," Working Papers halshs-00410746, HAL.
    8. Ergün, A. Tolga & Jun, Jongbyung, 2010. "Time-varying higher-order conditional moments and forecasting intraday VaR and Expected Shortfall," The Quarterly Review of Economics and Finance, Elsevier, vol. 50(3), pages 264-272, August.
    9. Marimoutou, Velayoudoum & Raggad, Bechir & Trabelsi, Abdelwahed, 2009. "Extreme Value Theory and Value at Risk: Application to oil market," Energy Economics, Elsevier, vol. 31(4), pages 519-530, July.
    10. Kulp-Tåg, Sofie, 2007. "An Empirical Investigation of Value-at-Risk in Long and Short Trading Positions," Working Papers 526, Hanken School of Economics.
    11. Gonzales-Martínez, Rolando, 2009. "La Gestión de Riesgo de Liquidez en Economías Emergentes: Un Modelo Valor-en-Riesgo (VaR) Paramétrico de Calibración Indirecta y una Aplicación al Sistema Financiero Boliviano
      [Liquidity Risk
      ," MPRA Paper 14247, University Library of Munich, Germany.
    12. CARPANTIER, Jean-François & DUFAYS, Arnaud, 2012. "Commodities volatility and the theory of storage," CORE Discussion Papers 2012037, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    13. Pérignon, Christophe & Deng, Zi Yin & Wang, Zhi Jun, 2008. "Do banks overstate their Value-at-Risk?," Journal of Banking & Finance, Elsevier, vol. 32(5), pages 783-794, May.

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