Measuring Tail Thickness Under GARCH and an Application to Extreme Exchange Rate Changes

Journal of Empirical Finance, Vol. 12, 2005

UC Berkeley IBER Finance Working Paper No. 297

30 Pages Posted: 22 Jan 2003 Last revised: 4 Oct 2009

See all articles by Terry Marsh

Terry Marsh

Quantal International Inc.

Niklas Wagner

Passau University

Date Written: September 1, 2003

Abstract

Accurate modeling of extreme price changes is vital to financial risk management. We examine the small sample properties of adaptive tail index estimators under the class of student-t marginal distribution functions including GARCH and propose a model-based bias-corrected estimation approach. Our simulation results indicate that bias strongly relates to the underlying model and may be positively as well as negatively signed. The empirical study of daily exchange rate changes reveals substantial differences in measured tail-thickness due to small sample bias. As a consequence, high quantile estimation may lead to a substantial underestimation of tail risk.

Keywords: fat tails, tail index, stationary marginal distribution, GARCH, Hill estimator, foreign exchange

JEL Classification: C13, C14, F31

Suggested Citation

Marsh, Terry and Wagner, Niklas F., Measuring Tail Thickness Under GARCH and an Application to Extreme Exchange Rate Changes (September 1, 2003). Journal of Empirical Finance, Vol. 12, 2005, UC Berkeley IBER Finance Working Paper No. 297, Available at SSRN: https://ssrn.com/abstract=360220 or http://dx.doi.org/10.2139/ssrn.360220

Terry Marsh

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

Niklas F. Wagner (Contact Author)

Passau University ( email )

Innstrasse 27
Passau, 94030
Germany

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