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Methods for evaluating value-at-risk estimates

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Author Info
Jose A. Lopez

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Abstract

Since 1998, U.S. commercial banks with significant trading activities have been required to hold capital against their defined market risk exposure. Under the "internal models" approach embodied in the current regulatory guidelines, the capital charges are a function of banks' own value-at-risk (VaR) estimates. VaR estimates are simply forecasts of the maximum portfolio loss that could occur over a given holding period with a specified confidence level. Clearly, the accuracy of these VaR estimates is of concern to both banks and their regulators. ; To date, two hypothesis-testing methods for evaluating VaR estimates have been proposed, namely, the binomial and the interval forecast methods. For these tests, the null hypothesis is that the VaR estimates in question exhibit a specified property that is characteristic of accurate VaR estimates. As shown in a simulation exercise, these tests generally have low power and are thus prone to misclassifying inaccurate VaR estimates as "acceptably accurate." ; An alternative evaluation method, based on regulatory loss functions, is proposed. Magnitude loss functions that assign quadratic numerical scores when observed portfolio losses exceed VaR estimates are shown to be particularly useful. Simulation results indicate that the loss function evaluation method is capable of distinguishing between VaR estimates generated by accurate and alternative VaR models. The additional information provided by this method as well as its flexibility with respect to the specification of the loss function make a reasonable case for its use in the regulatory evaluation of VaR estimates.

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Publisher Info
Article provided by Federal Reserve Bank of San Francisco in its journal Economic Review.

Volume (Year): (1999)
Issue (Month): ()
Pages: 3-17
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Handle: RePEc:fip:fedfer:y:1999:p:3-17:n:2

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Keywords: Risk ; Bank stocks;

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References listed on IDEAS
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.:
  1. 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.
  2. Francis X. Diebold & Todd A. Gunther & Anthony S. Tay, 1997. "Evaluating Density Forecasts," Center for Financial Institutions Working Papers 97-37, Wharton School Center for Financial Institutions, University of Pennsylvania. [Downloadable!]
    Other versions:
  3. Phillip Kearns & Adrian Pagan, 1997. "Estimating The Density Tail Index For Financial Time Series," The Review of Economics and Statistics, MIT Press, vol. 79(2), pages 171-175, May. [Downloadable!] (restricted)
  4. 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. [Downloadable!] (restricted)
  5. Francis X. Diebold & Jose A. Lopez, 1996. "Forecast Evaluation and Combination," NBER Technical Working Papers 0192, National Bureau of Economic Research, Inc. [Downloadable!] (restricted)
    Other versions:
  6. Jeremy Berkowitz, 1999. "Evaluating the forecasts of risk models," Finance and Economics Discussion Series 1999-11, Board of Governors of the Federal Reserve System (U.S.). [Downloadable!]
  7. Darryll Hendricks, 1996. "Evaluation of value-at-risk models using historical data," Economic Policy Review, Federal Reserve Bank of New York, issue Apr, pages 39-69. [Downloadable!]
  8. Darryll Hendricks, 1996. "Evaluation of value-at-risk models using historical data," Proceedings, Federal Reserve Bank of Chicago, issue May, pages 334-362.
  9. C. W.J. Granger & M. Hashem Pesaran, 1996. "A Decision Theoretic Approach to Forecast Evaluation," University of California at San Diego, Economics Working Paper Series 96-23, Department of Economics, UC San Diego.
    Other versions:
  10. Jose Lopez, 1998. "Methods for evaluating value-at-risk estimates," Research Paper 9802, Federal Reserve Bank of New York. [Downloadable!]
    Other versions:
  11. Matthew Pritsker, 1996. "Evaluating Value-at-Risk Methodologies: Accuracy versus Computational Time," Center for Financial Institutions Working Papers 96-48, Wharton School Center for Financial Institutions, University of Pennsylvania. [Downloadable!]
  12. Paul H. Kupiec & James M. O'Brien, 1995. "A pre-commitment approach to capital requirements for market risk," Proceedings, Federal Reserve Bank of Chicago, issue May, pages 552-562.
  13. Jose A. Lopez, 1997. "Regulatory evaluation of value-at-risk models," Staff Reports 33, Federal Reserve Bank of New York. [Downloadable!]
    Other versions:
  14. Paul H. Kupiec & James M. O'Brien, 1995. "A pre-commitment approach to capital requirements for market risk," Finance and Economics Discussion Series 95-36, Board of Governors of the Federal Reserve System (U.S.).
  15. 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.).
  16. 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.
  17. Darryll Hendricks & Beverly Hirtle, 1997. "Bank capital requirements for market risk: the internal models approach," Economic Policy Review, Federal Reserve Bank of New York, issue Dec, pages 1-12. [Downloadable!]
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