Physics – Condensed Matter – Statistical Mechanics
Scientific paper
2001-11-16
Quantitative Finance, 3, 231--250 (2003)
Physics
Condensed Matter
Statistical Mechanics
Latex document of 43 pages including 14 eps figures
Scientific paper
10.1088/1469-7688/3/4/301
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.
Malevergne Yannick
Sornette Didier
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