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Methods for evaluating value-at-risk estimates

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  • Jose A. Lopez

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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Bibliographic 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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  1. Jose A. Lopez, 1999. "Methods for evaluating value-at-risk estimates," Economic Review, Federal Reserve Bank of San Francisco, pages 3-17.
  2. Jose A. Lopez, 1997. "Regulatory evaluation of value-at-risk models," Research Paper 9710, Federal Reserve Bank of New York.
  3. Paul H. Kupiec & James M. O'Brien, 1995. "A pre-commitment approach to capital requirements for market risk," Proceedings 475, Federal Reserve Bank of Chicago.
  4. Francis X. Diebold & Jose A. Lopez, 1996. "Forecast Evaluation and Combination," NBER Technical Working Papers 0192, National Bureau of Economic Research, Inc.
  5. 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.
  6. 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.
  7. Francis X. Diebold & Todd A. Gunther & Anthony S. Tay, 1997. "Evaluating density forecasts," Working Papers 97-6, Federal Reserve Bank of Philadelphia.
  8. 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.
  9. 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.).
  10. Granger, C.W.J. & Pesaran, H., 1996. "A Decision_Theoretic Approach to Forecast Evaluation," Cambridge Working Papers in Economics 9618, Faculty of Economics, University of Cambridge.
  11. 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.
  12. 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.).
  13. 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.
  14. 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.
  15. 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.
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