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Beyond the Sample: Extreme Quantile and Probability Estimation

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Author Info
Jon Danielsson ()
Casper G. de Vries

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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 provides 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 threshold 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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Paper provided by Financial Markets Group in its series FMG Discussion Papers with number dp298.

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Date of creation: Jul 1998
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Handle: RePEc:fmg:fmgdps:dp298

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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. Hendry, David F., 1984. "Monte carlo experimentation in econometrics," Handbook of Econometrics, in: Z. Griliches† & M. D. Intriligator (ed.), Handbook of Econometrics, edition 1, volume 2, chapter 16, pages 937-976 Elsevier. [Downloadable!] (restricted)
  2. 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)
  3. 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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