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Extreme Value Theory for Tail-Related Risk Measures

Author

Listed:
  • Evis Këllezi

    (Department of Econometrics and FAME, University of Geneva,switzerland)

  • Manfred Gilli

    (Department of Econometrics, University of Geneva, Switzerland)

Abstract

Many fields of modern science and engineering have to deal with events which are rare but have significant consequences. Extreme value theory is considered to provide the basis for the statistical modeling of such extremes. The potential of extreme value theory applied to financial problems has only been recognized recently. This paper aims at introducing the fundamentals of extreme value theory as well as practical aspects for estimating and assessing statistical models for tail-related risk measures.

Suggested Citation

  • Evis Këllezi & Manfred Gilli, 2000. "Extreme Value Theory for Tail-Related Risk Measures," FAME Research Paper Series rp18, International Center for Financial Asset Management and Engineering.
    • Handle: RePEc:fam:rpseri:rp18
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    File URL: http://www.swissfinanceinstitute.ch/rp18.pdf
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    References listed on IDEAS

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    1. Francis X. Diebold & Til Schuermann & John D. Stroughair, 2000. "Pitfalls and Opportunities in the Use of Extreme Value Theory in Risk Management," Journal of Risk Finance, Emerald Group Publishing Limited, vol. 1(2), pages 30-35, January.
    2. 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.
    3. ROCKINGER, Michael & JONDEAU, Eric, 1999. "The Tail Behavior of Stock Returns: Emerging versus Mature Markets," HEC Research Papers Series 668, HEC Paris.
    4. McNeil, Alexander J. & Frey, Rudiger, 2000. "Estimation of tail-related risk measures for heteroscedastic financial time series: an extreme value approach," Journal of Empirical Finance, Elsevier, vol. 7(3-4), pages 271-300, November.
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    Citations

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    Cited by:

    1. Bystrom, Hans N. E., 2005. "Extreme value theory and extremely large electricity price changes," International Review of Economics & Finance, Elsevier, vol. 14(1), pages 41-55.
    2. Cristina Sommacampagna, 2002. "Stima del Value-at-Risk con il Filtro di Kalman," Rivista di Politica Economica, SIPI Spa, vol. 92(6), pages 147-174, November-.
    3. Bystrom, Hans N. E., 2004. "Managing extreme risks in tranquil and volatile markets using conditional extreme value theory," International Review of Financial Analysis, Elsevier, vol. 13(2), pages 133-152.
    4. Gupta, Anurag & Liang, Bing, 2005. "Do hedge funds have enough capital? A value-at-risk approach," Journal of Financial Economics, Elsevier, vol. 77(1), pages 219-253, July.
    5. Haque, Mahfuzul & Varela, Oscar & Hassan, M. Kabir, 2007. "Safety-first and extreme value bilateral U.S.-Mexican portfolio optimization around the peso crisis and NAFTA in 1994," The Quarterly Review of Economics and Finance, Elsevier, vol. 47(3), pages 449-469, July.
    6. Li, Wenwei & Hommel, Ulrich & Paterlini, Sandra, 2018. "Network topology and systemic risk: Evidence from the Euro Stoxx market," Finance Research Letters, Elsevier, vol. 27(C), pages 105-112.
    7. Ioan TalpoÅŸ & Cosmin Enache, 2007. "Public Finance And Extreme Events," Annales Universitatis Apulensis Series Oeconomica, Faculty of Sciences, "1 Decembrie 1918" University, Alba Iulia, vol. 1(9), pages 1-3.
    8. Novak, S.Y. & Beirlant, J., 2006. "The magnitude of a market crash can be predicted," Journal of Banking & Finance, Elsevier, vol. 30(2), pages 453-462, February.
    9. Lampros Kalyvas & Athanasios Sfetsos, 2006. "Does The Application Of Innovative Internal Models Diminish Regulatory Capital?," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 9(02), pages 217-226.

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    More about this item

    Keywords

    Extreme Value Theory; Generalized Pareto Distribution; Generalized Extreme Value Distribution; Quantile Estimation; Risk Measures; Maximum Likelihood Estimation; Profile Likelihood Confidence Intervals.;
    All these keywords.

    JEL classification:

    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • C19 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Other

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