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A review of backtesting and backtesting procedures

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  • Sean D. Campbell

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.

Suggested Citation

  • Sean D. Campbell, 2005. "A review of backtesting and backtesting procedures," Finance and Economics Discussion Series 2005-21, Board of Governors of the Federal Reserve System (U.S.).
    • Handle: RePEc:fip:fedgfe:2005-21
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    References listed on IDEAS

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    Cited by:

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    2. Jean-Francois Carpantier, 2010. "Commodities inventory effect," Working Papers hal-01821158, HAL.
    3. 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.
    4. Kimera Naradh & Retius Chifurira & Knowledge Chinhamu, 2022. "Analysis of stock exchange risk and currency in South African Financial Markets using stable parameter estimation," International Journal of Finance & Banking Studies, Center for the Strategic Studies in Business and Finance, vol. 11(1), pages 120-131, January.
    5. Durán Santomil, Pablo & Otero González, Luís & Martorell Cunill, Onofre & Merigó Lindahl, José M., 2018. "Backtesting an equity risk model under Solvency II," Journal of Business Research, Elsevier, vol. 89(C), pages 216-222.
    6. CARPANTIER, Jean-François & DUFAYS, Arnaud, 2012. "Commodities volatility and the theory of storage," LIDAM Discussion Papers CORE 2012037, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    7. Lööf, Hans & Stephan, Andreas, 2019. "The Impact of ESG on Stocks’ Downside Risk and Risk Adjusted Return," Working Paper Series in Economics and Institutions of Innovation 477, Royal Institute of Technology, CESIS - Centre of Excellence for Science and Innovation Studies.
    8. Wagner Piazza Gaglianone & Luiz Renato Lima & Oliver Linton & Daniel R. Smith, 2011. "Evaluating Value-at-Risk Models via Quantile Regression," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 29(1), pages 150-160, January.
    9. 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.
    10. Sabrina Khanniche, 2009. "Evaluation of Hedge Fund Returns Value at Risk Using GARCH Models," EconomiX Working Papers 2009-46, University of Paris Nanterre, EconomiX.
    11. Fries, Christian P. & Nigbur, Tobias & Seeger, Norman, 2017. "Displaced relative changes in historical simulation: Application to risk measures of interest rates with phases of negative rates," Journal of Empirical Finance, Elsevier, vol. 42(C), pages 175-198.
    12. Felipe de Oliveira & Sinézio Fernandes Maia, 2017. "Volatility Forecasting before the Subprime Crisis," EcoMod2017 10376, EcoMod.
    13. Codrut Florin Ivascu & Daniela Serban, 2023. "Value at Risk Estimation for Non-Gaussian Distributions," The Review of Finance and Banking, Academia de Studii Economice din Bucuresti, Romania / Facultatea de Finante, Asigurari, Banci si Burse de Valori / Catedra de Finante, vol. 15(2), pages 181-190, December.
    14. Vêlayoudom Marimoutou & Bechir Raggad & Abdelwahed Trabelsi, 2006. "Extreme Value Theory and Value at Risk : Application to Oil Market," Working Papers halshs-00410746, HAL.
    15. Escanciano, Juan Carlos & Pei, Pei, 2012. "Pitfalls in backtesting Historical Simulation VaR models," Journal of Banking & Finance, Elsevier, vol. 36(8), pages 2233-2244.
    16. 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 Manag," MPRA Paper 14247, University Library of Munich, Germany.
    17. 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 -.
    18. Evers, Corinna & Rohde, Johannes, 2014. "Model Risk in Backtesting Risk Measures," Hannover Economic Papers (HEP) dp-529, Leibniz Universität Hannover, Wirtschaftswissenschaftliche Fakultät.
    19. 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.
    20. Christophe HURLIN & Sessi TOKPAVI, 2006. "Backtesting VaR Accuracy: A Simple and Powerful Test," LEO Working Papers / DR LEO 268, Orleans Economics Laboratory / Laboratoire d'Economie d'Orleans (LEO), University of Orleans.
    21. Simon Fritzsch & Maike Timphus & Gregor Weiss, 2021. "Marginals Versus Copulas: Which Account For More Model Risk In Multivariate Risk Forecasting?," Papers 2109.10946, arXiv.org.

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