IDEAS home Printed from https://ideas.repec.org/p/aah/create/2009-35.html
   My bibliography  Save this paper

Evaluating Value-at-Risk Models with Desk-Level Data

Author

Listed:
  • Peter Christoffersen

    (McGill University and CREATES)

  • Jeremy Berkowitz

    (University of Houston)

  • Denis Pelletier

    (North Carolina State University)

Abstract

We present new evidence on disaggregated profit and loss (P/L) and Value-at-Risk (VaR) forecasts obtained from a large international commercial bank. Our dataset includes the actual daily P/L generated by four separate business lines within the bank. All four business lines are involved in securities trading and each is observed daily for a period of at least two years. Given this unique dataset, we provide an integrated, unifying framework for assessing the accuracy of VaR forecasts. We use a comprehensive Monte Carlo study to assess which of these many tests have the best finite-sample size and power properties. Our desk-level data set provides importance guidance for choosing realistic P/L generating processes in the Monte Carlo comparison of the various tests. The CaViaR test of Engle and Manganelli (2004) performs best overall but duration-based tests also perform well in many cases.

Suggested Citation

  • Peter Christoffersen & Jeremy Berkowitz & Denis Pelletier, 2008. "Evaluating Value-at-Risk Models with Desk-Level Data," CREATES Research Papers 2009-35, Department of Economics and Business Economics, Aarhus University.
  • Handle: RePEc:aah:create:2009-35
    as

    Download full text from publisher

    File URL: https://repec.econ.au.dk/repec/creates/rp/09/rp09_35.pdf
    Download Restriction: no
    ---><---

    Other versions of this item:

    References listed on IDEAS

    as
    1. Gordon J. Alexander & Alexandre M. Baptista, 2004. "A Comparison of VaR and CVaR Constraints on Portfolio Selection with the Mean-Variance Model," Management Science, INFORMS, vol. 50(9), pages 1261-1273, September.
    2. Jacob A. Mincer & Victor Zarnowitz, 1969. "The Evaluation of Economic Forecasts," NBER Chapters, in: Economic Forecasts and Expectations: Analysis of Forecasting Behavior and Performance, pages 3-46, National Bureau of Economic Research, Inc.
    3. James W. Taylor, 2005. "Generating Volatility Forecasts from Value at Risk Estimates," Management Science, INFORMS, vol. 51(5), pages 712-725, May.
    4. 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, June.
    5. Dufour, Jean-Marie, 2006. "Monte Carlo tests with nuisance parameters: A general approach to finite-sample inference and nonstandard asymptotics," Journal of Econometrics, Elsevier, vol. 133(2), pages 443-477, August.
    6. Robert F. Engle & Jeffrey R. Russell, 1998. "Autoregressive Conditional Duration: A New Model for Irregularly Spaced Transaction Data," Econometrica, Econometric Society, vol. 66(5), pages 1127-1162, September.
    7. Basak, Suleyman & Shapiro, Alexander, 2001. "Value-at-Risk-Based Risk Management: Optimal Policies and Asset Prices," The Review of Financial Studies, Society for Financial Studies, vol. 14(2), pages 371-405.
    8. Paramasamy, S., 1992. "On the multivariate Kolmogorov-Smirnov distribution," Statistics & Probability Letters, Elsevier, vol. 15(2), pages 149-155, September.
    9. Peter Christoffersen, 2004. "Backtesting Value-at-Risk: A Duration-Based Approach," Journal of Financial Econometrics, Oxford University Press, vol. 2(1), pages 84-108.
    10. Campbell, John Y & Shiller, Robert J, 1987. "Cointegration and Tests of Present Value Models," Journal of Political Economy, University of Chicago Press, vol. 95(5), pages 1062-1088, October.
    11. Andersen, Torben G. & Bollerslev, Tim & Christoffersen, Peter F. & Diebold, Francis X., 2006. "Volatility and Correlation Forecasting," Handbook of Economic Forecasting, in: G. Elliott & C. Granger & A. Timmermann (ed.), Handbook of Economic Forecasting, edition 1, volume 1, chapter 15, pages 777-878, Elsevier.
    12. Kiefer, Nicholas M, 1988. "Economic Duration Data and Hazard Functions," Journal of Economic Literature, American Economic Association, vol. 26(2), pages 646-679, June.
    13. Pérignon, Christophe & Smith, Daniel R., 2010. "The level and quality of Value-at-Risk disclosure by commercial banks," Journal of Banking & Finance, Elsevier, vol. 34(2), pages 362-377, February.
    14. Paul H. Kupiec, 1995. "Techniques for verifying the accuracy of risk measurement models," Finance and Economics Discussion Series 95-24, Board of Governors of the Federal Reserve System (U.S.).
    15. 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 841-862, November.
    16. Robert F. Engle & Simone Manganelli, 2004. "CAViaR: Conditional Autoregressive Value at Risk by Regression Quantiles," Journal of Business & Economic Statistics, American Statistical Association, vol. 22, pages 367-381, October.
    17. Domenico Cuoco & Hua He & Sergei Isaenko, 2008. "Optimal Dynamic Trading Strategies with Risk Limits," Operations Research, INFORMS, vol. 56(2), pages 358-368, April.
    18. G. Elliott & C. Granger & A. Timmermann (ed.), 2006. "Handbook of Economic Forecasting," Handbook of Economic Forecasting, Elsevier, edition 1, volume 1, number 1.
    19. Durlauf, Steven N., 1991. "Spectral based testing of the martingale hypothesis," Journal of Econometrics, Elsevier, vol. 50(3), pages 355-376, December.
    20. Domenico Cuoco & Hua He & Sergei Isaenko, 2008. "Optimal Dynamic Trading Strategies with Risk Limits," Operations Research, INFORMS, vol. 56(2), pages 358-368, April.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Nieto, Maria Rosa & Ruiz, Esther, 2016. "Frontiers in VaR forecasting and backtesting," International Journal of Forecasting, Elsevier, vol. 32(2), pages 475-501.
    2. James M. O'Brien & Pawel J. Szerszen, 2014. "An Evaluation of Bank VaR Measures for Market Risk During and Before the Financial Crisis," Finance and Economics Discussion Series 2014-21, Board of Governors of the Federal Reserve System (U.S.).
    3. Gordy, Michael B. & McNeil, Alexander J., 2020. "Spectral backtests of forecast distributions with application to risk management," Journal of Banking & Finance, Elsevier, vol. 116(C).
    4. Colletaz, Gilbert & Hurlin, Christophe & Pérignon, Christophe, 2013. "The Risk Map: A new tool for validating risk models," Journal of Banking & Finance, Elsevier, vol. 37(10), pages 3843-3854.
    5. Peter Christoffersen, 2004. "Backtesting Value-at-Risk: A Duration-Based Approach," Journal of Financial Econometrics, Oxford University Press, vol. 2(1), pages 84-108.
    6. O’Brien, James & Szerszeń, Paweł J., 2017. "An evaluation of bank measures for market risk before, during and after the financial crisis," Journal of Banking & Finance, Elsevier, vol. 80(C), pages 215-234.
    7. Escanciano, Juan Carlos & Pei, Pei, 2012. "Pitfalls in backtesting Historical Simulation VaR models," Journal of Banking & Finance, Elsevier, vol. 36(8), pages 2233-2244.
    8. Farkas, Walter & Fringuellotti, Fulvia & Tunaru, Radu, 2020. "A cost-benefit analysis of capital requirements adjusted for model risk," Journal of Corporate Finance, Elsevier, vol. 65(C).
    9. Alexander, Gordon J. & Baptista, Alexandre M. & Yan, Shu, 2012. "When more is less: Using multiple constraints to reduce tail risk," Journal of Banking & Finance, Elsevier, vol. 36(10), pages 2693-2716.
    10. Gaglianone, Wagner Piazza & Lima, Luiz Renato & Linton, Oliver & Smith, Daniel R., 2011. "Evaluating Value-at-Risk Models via Quantile Regression," Journal of Business & Economic Statistics, American Statistical Association, vol. 29(1), pages 150-160.
    11. 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.
    12. Frésard, Laurent & Pérignon, Christophe & Wilhelmsson, Anders, 2011. "The pernicious effects of contaminated data in risk management," Journal of Banking & Finance, Elsevier, vol. 35(10), pages 2569-2583, October.
    13. 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.
    14. Escanciano, Juan Carlos & Pei, Pei, 2012. "Pitfalls in backtesting Historical Simulation VaR models," Journal of Banking & Finance, Elsevier, vol. 36(8), pages 2233-2244.
    15. 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.
    16. 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.
    17. Jean-Paul Laurent & Hassan Omidi Firouzi, 2022. "Market Risk and Volatility Weighted Historical Simulation After Basel III," Working Papers hal-03679434, HAL.
    18. Takahashi, Makoto & Watanabe, Toshiaki & Omori, Yasuhiro, 2016. "Volatility and quantile forecasts by realized stochastic volatility models with generalized hyperbolic distribution," International Journal of Forecasting, Elsevier, vol. 32(2), pages 437-457.
    19. Pritsker, Matthew, 2006. "The hidden dangers of historical simulation," Journal of Banking & Finance, Elsevier, vol. 30(2), pages 561-582, February.
    20. Christophe Hurlin & Christophe Pérignon, 2012. "Margin Backtesting," Working Papers halshs-00746274, HAL.

    More about this item

    Keywords

    Risk Management; Backtesting; Volatility; Disclosure;
    All these keywords.

    JEL classification:

    • 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

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:aah:create:2009-35. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: the person in charge (email available below). General contact details of provider: http://www.econ.au.dk/afn/ .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.