Self-exciting Extreme Value Models for Stock Market Crashes

  • Rodrigo Herrera
  • Bernhard Schipp


We demonstrate the usefulness of Extreme value Theory (EVT) to evaluate magnitudes of stock market crashes and provide some extensions. A common practice in EVT is to compute either unconditional quantiles of the loss distribution or conditional methods linking GARCH models to EVT. Our approach combines self-exciting models for exceedances over a given threshold with a marked dependent process for estimating the tail of loss distributions. The corresponding models allow to adopt ex-ante estimation of two risk measures in different quantiles to assess the expected frequency of different crashes of important stock market indices. The paper concludes with a backtesting estimation of the magnitude of major stock market crashes in financial history from one day before an important crash until one year later. The results show that this approach provides better estimates of risk measures than the classical methods and is moreover able to use available data in a more efficient way.


Risk Measure Generalize Pareto Distribution Conditional Intensity Expect Shortfall Extreme Value Theory 
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  1. 1.
    Beirlant, J., Goegebeu, Y., Segers, J., Teugels, J., Waal, D.D.: Statistics of Extremes: Theory and Applications. Wiley, New York (2004)MATHGoogle Scholar
  2. 2.
    Chavez-Demoulin, V., Davison, A., McNeil, A.: A point process approach to value-at-risk estimation. Quant. Fin. 5, 227–234 (2005)MATHCrossRefMathSciNetGoogle Scholar
  3. 3.
    Chavez-Demoulin, V., Sardy, S.: A Bayesian nonparametric peaks over threshold method to estimate risk measures of a nonstationary financial time series. Research Paper, Department of Mathematics, ETH, Zürich (2004)Google Scholar
  4. 4.
    Cotter, J., Dowd, K.: Extreme spectral risk measures: An application to futures clearinghouse margin requirements. J. Bank. Fin 30, 3469–3485 (2006)CrossRefGoogle Scholar
  5. 5.
    Daley, D., Vere-Jones, D.: An Introduction to the Theory of Point Processes. Springer, Berlin (2003)MATHGoogle Scholar
  6. 6.
    Embrechts, P., Kluppelberg, C., Mikosch, T.: Modeling Extremal Events. Springer, Berlin (1997)Google Scholar
  7. 7.
    Falk, M., Hüsler, J., Reiss, R.: Laws of Small Numbers: Extremes and Rare Events. Birkhäuser, Boston (2004)MATHGoogle Scholar
  8. 8.
    Ferro, C.A.T., Segers, J.: Inference for clusters of extreme values. J. Roy. Stat. Soc. B 65, 545–556 (2003)MATHCrossRefMathSciNetGoogle Scholar
  9. 9.
    Hawkes, A.: Spectra of some self-exciting and mutually exciting point processes. Biometrika 58, 379–402 (1971)CrossRefMathSciNetGoogle Scholar
  10. 10.
    Kagan, Y.Y., Knopoff, L.: Statistical short-term earthquake prediction. Science 235, 1563–1467 (1987)CrossRefGoogle Scholar
  11. 11.
    Longin, F., Solnik, B.: Extreme correlation of international equity markets. J. Finance 56, 649–676 (2001)CrossRefGoogle Scholar
  12. 12.
    Matthys, G., Beirlant, J.: Extreme quantile estimation for heavy tailed distributions. Technical Report, Universitair centrum voor Statistiek, Katholieke Universiteit Leuven, Leuven, Belgium (2001)Google Scholar
  13. 13.
    McNeil, A., Frey, R.: Estimation of tail-related risk measures for het-eroscedastic financial time series: an extreme value approach. J. Emp. Finance 7, 271–300 (2000)CrossRefGoogle Scholar
  14. 14.
    McNeil, A.J.: On extremes and crashes. Risk 11, 99–104 (1998)Google Scholar
  15. 15.
    McNeil, A.J., Chavez-Demoulin, V.: Self-exciting processes for extremes in financial time series. Cornell University, Financial Engineering seminar, Talk (2006)Google Scholar
  16. 16.
    McNeil, A.J., Frey, R., Embrechts, P.: Quantitative Risk Management: Concepts, Techniques, and Tools. Princeton University Press, Princeton (2005)MATHGoogle Scholar
  17. 17.
    Novak, S.Y.: Value at risk and the “Black Monday” crash. MUBS Discussion Paper 25, Middlesex University, UK (2004)Google Scholar
  18. 18.
    Ogata, Y.: Statistical models for earthquake occurrences and residual analysis for point processes. J. Am. Stat. Assoc. 83, 9–27 (1988)CrossRefGoogle Scholar
  19. 19.
    Smith, R.: Extreme value analysis of environmental time series: An application to trend detection in ground-level ozone. Stat. Sci. 44, 367–393 (1989)CrossRefGoogle Scholar

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© Physica-Verlag Heidelberg 2009

Authors and Affiliations

  1. 1.Fakultät WirtschaftswissenschaftenTechnische Universität DresdenDresdenGermany

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