statistique, théorie et gestion de portefeuille - Docs at ISFA

Testing the Gaussian Copula Hypothesis
for Financial Assets Dependences ∗
Y. Malevergne 1,2 and D. Sornette 1,3
1 Laboratoire de Physique de la Matière Condensée CNRS UMR 6622
Université de Nice-Sophia Antipolis, 06108 Nice Cedex 2, France
2 Institut de Science Financière et d’Assurances - Université Lyon I
43, Bd du 11 Novembre 1918, 69622 Villeurbanne Cedex
3 Institute of Geophysics and Planetary Physics and Department of Earth and Space Science
University of California, Los Angeles, California 90095, USA
Corresponding author: D. Sornette
Institute of Geophysics and Planetary Physics
University of California, Los Angeles, California 90095, USA
email: sornette@ess.ucla.edu tel: (310) 825 28 63 Fax: (310) 206 30 51
Submitted to Quantitative Finance
Abstract
Using one of the key property of copulas that they remain invariant under an arbitrary monotonous
change of variable, we investigate the null hypothesis that the dependence between financial assets
can be modeled by the Gaussian copula. We find that most pairs of currencies and pairs of major
stocks are compatible with the Gaussian copula hypothesis, while this hypothesis can be rejected for
the dependence between pairs of commodities (metals). Notwithstanding the apparent qualification
of the Gaussian copula hypothesis for most of the currencies and the stocks, a non-Gaussian copula,
such as the Student’s copula, cannot be rejected if it has sufficiently many “degrees of freedom”. As a
consequence, it may be very dangerous to embrace blindly the Gaussian copula hypothesis, especially
when the correlation coefficient between the pair of asset is too high as the tail dependence neglected
by the Gaussian copula can be as large as 0.6, i.e., three out five extreme events which occur in unison
are missed.
JEL Classification: C12, C15, F31, G19
Keywords: Copulas, Dependence Modelisation, Risk Management, Tail Dependence.
∗ We acknowledge helpful discussions and exchanges with J. Andersen, P. Embrechts, J.P. Laurent, F. Lindskog, V. Pisarenko
and R. Valkanov. This work was partially supported by the James S. Mc Donnell Foundation 21st century scientist
award/studying complex system.
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