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From Value at Risk to Stress Testing: The Extreme Value Approach

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  • Longin, François
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    Abstract

    This article presents an application of extreme value theory to compute the value at risk of a market position. In statistics, extremes of a random process refer to the lowest observation (the minimum) and to the highest observation (the maximum) over a given time-period. Extreme value theory gives some interesting results about the distribution of extreme returns. In particular, the limiting distribution of extreme returns observed over a long time-period is largely independent of the distribution of returns itself. In financial markets, extreme price movements correspond to market corrections during ordinary periods, and also to stock market crashes, bond market collapses or foreign exchange crises during extraordinary periods. An approach based on extreme values to compute the VaR thus covers market conditions ranging from the usual environment considered by the existing VaR methods to the financial crises which are the focus of stress testing. Univariate extreme value theory is used to compute the VaR of a fully-aggregated position while multivariate extreme value theory is used to compute the VaR of a position decomposed on risk factors.

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    Bibliographic Info

    Paper provided by C.E.P.R. Discussion Papers in its series CEPR Discussion Papers with number 2161.

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    Date of creation: May 1999
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    Handle: RePEc:cpr:ceprdp:2161

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    Related research

    Keywords: Aggregation of Risks; Capital Requirements; extreme value theory; Financial Crises; Financial Regulation; Measure of Risk; Risk Management; Stress Testing; Value at Risk;

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    References

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    1. Stoll, Hans R. & Whaley, Robert E., 1990. "The Dynamics of Stock Index and Stock Index Futures Returns," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 25(04), pages 441-468, December.
    2. Jón Daníelsson & Casper G. de Vries, 1998. "Value-at-Risk and Extreme Returns," Tinbergen Institute Discussion Papers 98-017/2, Tinbergen Institute.
    3. Andrew W. Lo & A. Craig MacKinlay, 1991. "An Econometric Analysis of Nonsynchronous Trading," NBER Working Papers 2960, National Bureau of Economic Research, Inc.
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    5. Longin, Francois M, 1996. "The Asymptotic Distribution of Extreme Stock Market Returns," The Journal of Business, University of Chicago Press, vol. 69(3), pages 383-408, July.
    6. Loretan, Mico & Phillips, Peter C. B., 1994. "Testing the covariance stationarity of heavy-tailed time series: An overview of the theory with applications to several financial datasets," Journal of Empirical Finance, Elsevier, vol. 1(2), pages 211-248, January.
    7. Huisman, R. & Koedijik, K.G. & Pownall, R.A.J., 1998. "VaR-x: Fat Tails in Financial Risk Management," Papers 98-54, Southern California - School of Business Administration.
    8. Berger, Allen N. & Herring, Richard J. & Szego, Giorgio P., 1995. "The role of capital in financial institutions," Journal of Banking & Finance, Elsevier, vol. 19(3-4), pages 393-430, June.
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    11. M.J.B. Hall, 1996. "The amendment to the capital accord to incorporate market risk," BNL Quarterly Review, Banca Nazionale del Lavoro, vol. 49(197), pages 271-277.
    12. 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.).
    13. Patricia Jackson & David Maude & William Perraudin, 1998. "Bank Capital and Value at Risk," Bank of England working papers 79, Bank of England.
    14. Robert C. Merton & André Perold, 1993. "Theory Of Risk Capital In Financial Firms," Journal of Applied Corporate Finance, Morgan Stanley, vol. 6(3), pages 16-32.
    15. M.J.B. Hall, 1996. "The amendment to the capital accord to incorporate market risk," Banca Nazionale del Lavoro Quarterly Review, Banca Nazionale del Lavoro, vol. 49(197), pages 271-277.
    16. Dimson, Elroy & Marsh, Paul, 1997. "Stress tests of capital requirements," Journal of Banking & Finance, Elsevier, vol. 21(11-12), pages 1515-1546, December.
    17. Longin, Francois M, 1997. "The Threshold Effect in Expected Volatility: A Model Based on Asymmetric Information," Review of Financial Studies, Society for Financial Studies, vol. 10(3), pages 837-69.
    18. de Haan, Laurens & Resnick, Sidney I. & Rootzén, Holger & de Vries, Casper G., 1989. "Extremal behaviour of solutions to a stochastic difference equation with applications to arch processes," Stochastic Processes and their Applications, Elsevier, vol. 32(2), pages 213-224, August.
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    Cited by:
    1. Cotter, John, 2000. "Margin Exceedences for European Stock Index Futures using Extreme Value Theory," MPRA Paper 3534, University Library of Munich, Germany, revised 2001.
    2. Martin Cihak, 2004. "Stress Testing: A Review of Key Concepts," Research and Policy Notes 2004/02, Czech National Bank, Research Department.

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