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Robust Estimators in Generalized Pareto Models

Author

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  • Peter Ruckdeschel

    (Fraunhofer ITWM, Department of Financial Mathematics, Dept. of Mathematics, Univerisity of Kaiserslautern)

  • Nataliya Horbenko

    (Fraunhofer ITWM, Department of Financial Mathematics, Dept. of Mathematics, Univerisity of Kaiserslautern)

Abstract

This paper deals with optimally-robust parameter estimation in generalized Pareto distributions (GPDs). These arise naturally in many situations where one is interested in the behavior of extreme events as motivated by the Pickands-Balkema-de Haan extreme value theorem (PBHT). The application we have in mind is calculation of the regulatory capital required by Basel II for a bank to cover operational risk. In this context the tail behavior of the underlying distribution is crucial. This is where extreme value theory enters, suggesting to estimate these high quantiles parameterically using, e.g. GPDs. Robust statistics in this context offers procedures bounding the influence of single observations, so provides reliable inference in the presence of moderate deviations from the distributional model assumptions, respectively from the mechanisms underlying the PBHT.

Suggested Citation

  • Peter Ruckdeschel & Nataliya Horbenko, 2010. "Robust Estimators in Generalized Pareto Models," Papers 1005.1476, arXiv.org, revised Sep 2011.
  • Handle: RePEc:arx:papers:1005.1476
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    File URL: http://arxiv.org/pdf/1005.1476
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    1. Hans U. Gerber & Hlias S. W. Shiu, 1996. "Martingale Approach To Pricing Perpetual American Options On Two Stocks," Mathematical Finance, Wiley Blackwell, vol. 6(3), pages 303-322.
    2. Windcliff, H. & Forsyth, P. A. & Vetzal, K. R., 2001. "Valuation of segregated funds: shout options with maturity extensions," Insurance: Mathematics and Economics, Elsevier, vol. 29(1), pages 1-21, August.
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