Testing the Gaussian Copula Hypothesis for Financial Assets Dependences

Quantitative Finance, Vol. 3, pp. 231-250, 2003

43 Pages Posted: 21 Nov 2001 Last revised: 7 Apr 2009

See all articles by Yannick Malevergne

Yannick Malevergne

Université Paris I Panthéon-Sorbonne - Laboratoire PRISM; Labex ReFi

Didier Sornette

ETH Zürich - Department of Management, Technology, and Economics (D-MTEC); Swiss Finance Institute; Southern University of Science and Technology; Tokyo Institute of Technology

Date Written: 2003

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, specially 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.

Keywords: Copulas, Dependence Modelisation, Risk Management, Tail Dependence

JEL Classification: C12, C15, F31, G19

Suggested Citation

Malevergne, Yannick and Sornette, Didier, Testing the Gaussian Copula Hypothesis for Financial Assets Dependences (2003). Quantitative Finance, Vol. 3, pp. 231-250, 2003, Available at SSRN: https://ssrn.com/abstract=291140 or http://dx.doi.org/10.2139/ssrn.291140

Yannick Malevergne

Université Paris I Panthéon-Sorbonne - Laboratoire PRISM ( email )

17 rue de la Sorbonne
Paris, 75005
France

HOME PAGE: http://perso.univ-paris1.fr/ymalevergn

Labex ReFi ( email )

79 avenue de la République
Paris, 75011
France

Didier Sornette (Contact Author)

ETH Zürich - Department of Management, Technology, and Economics (D-MTEC) ( email )

Scheuchzerstrasse 7
Zurich, ZURICH CH-8092
Switzerland
41446328917 (Phone)
41446321914 (Fax)

HOME PAGE: http://www.er.ethz.ch/

Swiss Finance Institute

c/o University of Geneva
40, Bd du Pont-d'Arve
CH-1211 Geneva 4
Switzerland

Southern University of Science and Technology

1088 Xueyuan Avenue
Shenzhen, Guangdong 518055
China

Tokyo Institute of Technology

2-12-1 O-okayama, Meguro-ku
Tokyo 152-8550, 52-8552
Japan

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