Multivariate Extremes, Aggregation and Risk Estimation

Posted: 28 Sep 2001

See all articles by Ulrich A. Müller

Ulrich A. Müller

Olsen & Associates

Hoskuldur Ari Hauksson

RWE Trading UK Ltd

Michel M. Dacorogna


Thomas Domenig

Zurcher Kantonalbank

Gennady Samorodnitsky

Cornell University

Multiple version iconThere are 2 versions of this paper


We briefly introduce some basic facts about multivariate extreme value theory and present some new results regarding finite aggregates and multivariate extreme value distributions. Based on our results high frequency data can considerably improve quality of estimates of extreme movements in financial markets. Secondly we present an empirical exploration of what the tails really look like for four foreign exchange rates sampled at varying frequencies. Both temporal and spatial dependence is considered. In particular we estimate the spectral measure, which along with the tail index, completely determines the extreme value distribution. Lastly we apply our results to the problem of portfolio optimization or risk minimization. We analyze how the expected shortfall and VaR scale with time horizon and find that this scaling is not by a factor of square root of time as is frequently used, but by a different power of time. We show that the accuracy of risk estimation can be drastically improved by using hourly or bihourly data.

JEL Classification: C14, F31, G11

Suggested Citation

Müller, Ulrich A. and Hauksson, Hoskuldur Ari and Dacorogna, Michel M. and Domenig, Thomas and Samorodnitsky, Gennady, Multivariate Extremes, Aggregation and Risk Estimation. Available at SSRN:

Ulrich A. Müller (Contact Author)

Olsen & Associates ( email )

Seefeldstrasse 233
CH-8008 Zurich
+41 (1) 386 48 16 (Phone)
+41 (1) 422 22 82 (Fax)

Hoskuldur Ari Hauksson

RWE Trading UK Ltd ( email )

130 Wood Street
London EC2V 6DL
United Kingdom

Michel M. Dacorogna

DEAR-Consulting ( email )

Scheuchzerstrasse 160
Zurich, 8057
+41795447327 (Phone)

Thomas Domenig

Zurcher Kantonalbank ( email )

Zurich 8000

Gennady Samorodnitsky

Cornell University ( email )

School of Operations Research and Industrial Engineering; Department of Statistical Science
Ithaca, NY 14853
United States

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