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Scaling of High-Quantile Estimators

Published online by Cambridge University Press:  14 July 2016

Matthias Degen*
Affiliation:
ETH Zürich
Paul Embrechts*
Affiliation:
ETH Zürich and Swiss Finance Institute
*
Postal address: Department of Mathematics, ETH Zürich, Raemistrasse 101, CH-8092 Zürich, Switzerland.
Postal address: Department of Mathematics, ETH Zürich, Raemistrasse 101, CH-8092 Zürich, Switzerland.
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Abstract

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Enhanced by the global financial crisis, the discussion about an accurate estimation of regulatory (risk) capital a financial institution needs to hold in order to safeguard against unexpected losses has become highly relevant again. The presence of heavy tails in combination with small sample sizes turns estimation at such extreme quantile levels into an inherently difficult statistical issue. We discuss some of the problems and pitfalls that may arise. In particular, based on the framework of second-order extended regular variation, we compare different high-quantile estimators and propose methods for the improvement of standard methods by focusing on the concept of penultimate approximations.

Type
Research Papers
Copyright
Copyright © Applied Probability Trust 2011 

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