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Beyond the sample: extreme quantile and probability estimation

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  • Danielsson, Jon
  • Vries, Casper

Abstract

Economic problems such as large claims analysis in insurance and value-at-risk in fi- nance, 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 sub- sample 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.

Suggested Citation

  • Danielsson, Jon & Vries, Casper, 1998. "Beyond the sample: extreme quantile and probability estimation," LSE Research Online Documents on Economics 119141, London School of Economics and Political Science, LSE Library.
    • Handle: RePEc:ehl:lserod:119141
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    References listed on IDEAS

    as
    1. 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.
    2. 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.
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    More about this item

    Keywords

    extreme value theory; tail estimation; risk analysis;
    All these keywords.

    JEL classification:

    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General

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