On Adaptive Tail Index Estimation for Financial Return Models

UC Berkeley Working Paper No. RPF-295

31 Pages Posted: 23 Jan 2001

See all articles by Niklas Wagner

Niklas Wagner

Passau University

Terry Marsh

Quantal International Inc.

Date Written: January 2002

Abstract

Estimation of the tail index of stationary, fat-tailed return distributions is non-trivial since the well-known Hill estimator is optimal only under iid draws from an exact Pareto model. We provide a small sample simulation study of recently suggested adaptive estimators under ARCH-type dependence. The Hill estimator's performance is found to be dominated by a ratio estimator. Dependence increases estimation error which can remain substantial even in larger data sets. As small sample bias is related to the magnitude of the tail index, recent standard applications may have overestimated (underestimated) the risk of assets with low (high) degrees of fat-tailedness.

Keywords: Fat-tails, tail index of stationary marginal distributions, Hill estimator, minimal AMSE

JEL Classification: C13, C14

Suggested Citation

Wagner, Niklas F. and Marsh, Terry, On Adaptive Tail Index Estimation for Financial Return Models (January 2002). UC Berkeley Working Paper No. RPF-295, Available at SSRN: https://ssrn.com/abstract=249551 or http://dx.doi.org/10.2139/ssrn.249551

Niklas F. Wagner

Passau University ( email )

Innstrasse 27
Passau, 94030
Germany

Terry Marsh (Contact Author)

Quantal International Inc. ( email )

Two Embarcadero Center
8th Floor
San Francisco, CA 94111
United States
415-744-5301 (Phone)

HOME PAGE: http://www.quantal.com

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