Beyond the Sample: Extreme Quantile and Probability Estimation
AbstractEconomic problems such as large claims analysis in insurance and value-at-risk in finance, requireassessment of the probability P of extreme realizations Q. This paper provided a semi-parametricmethod for estimation of extreme (P, Q) combinations for data with heavy tails. We solve the longstanding problem of estimating the sample treshold of where the tail of the distribution starts. This isaccomplished 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 wouldonly provide convergence in distribution. This permits a complete and comprehensive treatment ofextreme (P, Q) estimation.
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Bibliographic InfoPaper provided by Tinbergen Institute in its series Tinbergen Institute Discussion Papers with number 98-016/2.
Date of creation: 16 Feb 1998
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Extreme value theory; tail estimation; risk analysis;
Other versions of this item:
- Jon Danielsson & Casper G. de Vries, 1998. "Beyond the Sample: Extreme Quantile and Probability Estimation," FMG Discussion Papers, Financial Markets Group dp298, Financial Markets Group.
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- Koedijk, C.G. & Schafgans, M.M.A. & Vries, C.G. de, 1990. "The tail index of exchange rate returns," Open Access publications from Tilburg University urn:nbn:nl:ui:12-3108722, Tilburg University.
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MIT Press, vol. 73(1), pages 18-24, February.
- Dennis Jansen & Casper de Vries, 1988. "On the frequency of large stock returns: putting booms and busts into perspective," Working Papers, Federal Reserve Bank of St. Louis 1989-006, Federal Reserve Bank of St. Louis.
- Hendry, David F., 1984. "Monte carlo experimentation in econometrics," Handbook of Econometrics, Elsevier, in: Z. Griliches† & M. D. Intriligator (ed.), Handbook of Econometrics, edition 1, volume 2, chapter 16, pages 937-976 Elsevier.
- 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.
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