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Beyond the Sample: Extreme Quantile and Probability Estimation

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Author Info
Jón Daníelsson () (London School of Economics, University of Iceland)
Casper G. de Vries () (Erasmus University Rotterdam)

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Abstract

Economic problems such as large claims analysis in insurance and value-at-risk in finance, require assessment of the probability P of extreme realizations Q. This paper provided a semi-parametric method for estimation of extreme (P, Q) combinations for data with heavy tails. We solve the long standing problem of estimating the sample treshold of where the tail of the distribution starts. This is accomplished by the combination of a control variate type device and a subsample bootstrap technique. The subsample bootstrap attains convergence in probability, whereas the full sample bootstrap would only provide convergence in distribution. This permits a complete and comprehensive treatment of extreme (P, Q) estimation.

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Publisher Info
Paper provided by Tinbergen Institute in its series Tinbergen Institute Discussion Papers with number 98-016/2.

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Date of creation: 16 Feb 1998
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Handle: RePEc:dgr:uvatin:19980016

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Web page: http://www.tinbergen.nl/

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Keywords: Extreme value theory tail estimation risk analysis

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References listed on IDEAS
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
  1. Phillip Kearns & Adrian Pagan, 1997. "Estimating The Density Tail Index For Financial Time Series," The Review of Economics and Statistics, MIT Press, vol. 79(2), pages 171-175, May. [Downloadable!] (restricted)
  2. 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. [Downloadable!] (restricted)
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(explanations, Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.)

  1. R.W.J. van den Goorbergh & P.J.G. Vlaar, 1999. "Value-at-Risk Analysis of Stock Returns Historical Simulation,Variance Techniques or Tail Index Estimation?," DNB Staff Reports (discontinued) 40, Netherlands Central Bank. [Downloadable!]
    Other versions:
  2. Francis X. Diebold & Til Schuermann & John D. Stroughair, 1998. "Pitfalls and Opportunities in the Use of Extreme Value Theory in Risk Management," Center for Financial Institutions Working Papers 98-10, Wharton School Center for Financial Institutions, University of Pennsylvania. [Downloadable!]
    Other versions:
  3. Simone Manganelli & Robert F. Engle, 2001. "Value at risk models in finance," Working Paper Series 075, European Central Bank. [Downloadable!]
  4. Sebastian Schich, 2004. "European stock market dependencies when price changes are unusually large," Applied Financial Economics, Taylor and Francis Journals, vol. 14(3), pages 165-177, February. [Downloadable!] (restricted)
  5. Kilic, Ekrem, 2006. "Violation duration as a better way of VaR model evaluation : evidence from Turkish market portfolio," MPRA Paper 5610, University Library of Munich, Germany. [Downloadable!]
  6. Marcia M. A. Schafgans, 2000. "On Intercept Estimation in the Sample Selection Model," Econometric Society World Congress 2000 Contributed Papers 0730, Econometric Society. [Downloadable!]
  7. Tsourti, Zoi & Panaretos, John, 2004. "Extreme Value Analysis of Teletraffic Data," MPRA Paper 6391, University Library of Munich, Germany. [Downloadable!]
    Other versions:
  8. Cotter, John, 2004. "Downside Risk for European Equity Markets," MPRA Paper 3537, University Library of Munich, Germany. [Downloadable!]
    Other versions:
  9. R.W.J. van den Goorbergh, 1999. "Value-at-Risk and least squares tail index estimation," WO Research Memoranda (discontinued) 578, Netherlands Central Bank, Research Department. [Downloadable!]
  10. Lucas, Andr‚ & Straetmans, Stefan & Klaassen, Pieter, 1999. "Tail behavior of credit loss distributions," Serie Research Memoranda 0060, VU University Amsterdam, Faculty of Economics, Business Administration and Econometrics. [Downloadable!]
  11. Marcia M Schafgans & Victoria Zinde-Walsh, 2000. "On Intercept Estimation in the Sample Selection Model," STICERD - Econometrics Paper Series /2000/380, Suntory and Toyota International Centres for Economics and Related Disciplines, LSE. [Downloadable!]
    Other versions:
  12. Guang Bi & David E. Giles, 2007. "An Application of Extreme Value Theory to U.S. Movie Box Office Returns," Econometrics Working Papers 0705, Department of Economics, University of Victoria. [Downloadable!]
  13. Tsourti, Zoi & Panaretos, John, 2001. "Extreme Value Index Estimators and Smoothing Alternatives: Review and Simulation Comparison," MPRA Paper 6384, University Library of Munich, Germany. [Downloadable!]
  14. Silvia Caserta & Jon Danielsson & Casper G. de Vries, 1998. "Abnormal Returns, Risk, and Options in Large Data Sets," Tinbergen Institute Discussion Papers 98-107/2, Tinbergen Institute. [Downloadable!]
  15. Cotter, John, 2000. "Margin Exceedences for European Stock Index Futures using Extreme Value Theory," MPRA Paper 3534, University Library of Munich, Germany, revised 2001. [Downloadable!]
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  16. Tsourti, Zoi & Panaretos, John, 2003. "Extreme Value Index Estimators and Smoothing Alternatives: A Critical Review," MPRA Paper 6390, University Library of Munich, Germany. [Downloadable!]
  17. Niklas Wagner & Terry Marsh, 2000. "On Adaptive Tail Index Estimation for Financial Return Models," Research Program in Finance, Working Paper Series 1000, Research Program in Finance, Institute for Business and Economic Research, UC Berkeley. [Downloadable!]
    Other versions:
  18. Robert Engle & Simone Manganelli, 2000. "CAViaR: Conditional Autoregressive Value at Risk by Regression Quantiles," Econometric Society World Congress 2000 Contributed Papers 0841, Econometric Society. [Downloadable!]
    Other versions:
  19. Robert F. Engle & Simone Manganelli, 1999. "CAViaR: Conditional Value at Risk by Quantile Regression," NBER Working Papers 7341, National Bureau of Economic Research, Inc. [Downloadable!] (restricted)
  20. Carmela E. Quintos & Zhenhong Fan & Peter C.B. Phillips, 2000. "Structural Change in Tail Behavior and the Asian Financial Crisis," Cowles Foundation Discussion Papers 1283, Cowles Foundation, Yale University. [Downloadable!]
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