IDEAS home Printed from
   My bibliography  Save this paper

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


  • Longin, François


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.

Suggested Citation

  • Longin, François, 1999. "From Value at Risk to Stress Testing: The Extreme Value Approach," CEPR Discussion Papers 2161, C.E.P.R. Discussion Papers.
  • Handle: RePEc:cpr:ceprdp:2161

    Download full text from publisher

    File URL:
    Download Restriction: CEPR Discussion Papers are free to download for our researchers, subscribers and members. If you fall into one of these categories but have trouble downloading our papers, please contact us at

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    1. Jansen, Dennis W & de Vries, Casper G, 1991. "On the Frequency of Large Stock Returns: Putting Booms and Busts into Perspective," The Review of Economics and Statistics, MIT Press, vol. 73(1), pages 18-24, February.
    2. Lo, Andrew W. & Craig MacKinlay, A., 1990. "An econometric analysis of nonsynchronous trading," Journal of Econometrics, Elsevier, vol. 45(1-2), pages 181-211.
    3. Dimson, Elroy & Marsh, Paul, 1997. "Stress tests of capital requirements," Journal of Banking & Finance, Elsevier, vol. 21(11-12), pages 1515-1546, December.
    4. 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.
    5. 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.
    6. 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.).
    7. 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.
    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.
    9. 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.
    10. 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 837-869.
    11. 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.
    12. Patricia Jackson & David Maude & William Perraudin, 1998. "Bank Capital and Value at Risk," Bank of England working papers 79, Bank of England.
    13. 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.
    14. Philippe Artzner & Freddy Delbaen & Jean-Marc Eber & David Heath, 1999. "Coherent Measures of Risk," Mathematical Finance, Wiley Blackwell, vol. 9(3), pages 203-228.
    15. 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.
    16. Hamao, Yasushi & Masulis, Ronald W & Ng, Victor, 1990. "Correlations in Price Changes and Volatility across International Stock Markets," Review of Financial Studies, Society for Financial Studies, vol. 3(2), pages 281-307.
    Full references (including those not matched with items on IDEAS)


    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.

    Cited by:

    1. Cotter, John, 2001. "Margin exceedences for European stock index futures using extreme value theory," Journal of Banking & Finance, Elsevier, vol. 25(8), pages 1475-1502, August.
    2. Martin Cihak, 2004. "Stress Testing: A Review of Key Concepts," Research and Policy Notes 2004/02, Czech National Bank, Research Department.

    More about this item


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

    JEL classification:

    • C51 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Construction and Estimation
    • G28 - Financial Economics - - Financial Institutions and Services - - - Government Policy and Regulation


    Access and download statistics


    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:cpr:ceprdp:2161. See general information about how to correct material in RePEc.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (). General contact details of provider: .

    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 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.

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

    IDEAS is a RePEc service hosted by the Research Division of the Federal Reserve Bank of St. Louis . RePEc uses bibliographic data supplied by the respective publishers.