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Testing the Gaussian Copula Hypothesis for Financial Assets Dependences

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  • Y. Malevergne

    (ISFA-Lyon and Univ. Nice/CNRS)

  • D. Sornette

    (Univ. Nice/CNRS and UCLA)

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.

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Paper provided by arXiv.org in its series Papers with number cond-mat/0111310.

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Date of creation: Nov 2001
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Publication status: Published in Quantitative Finance, 3, 231--250 (2003)
Handle: RePEc:arx:papers:cond-mat/0111310

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  9. Joshua Rosenberg, 1999. "Semiparametric Pricing of Multivariate Contingent Claims," New York University, Leonard N. Stern School Finance Department Working Paper Seires 99-028, New York University, Leonard N. Stern School of Business-.
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