Investigating Extreme Dependences: Concepts and Tools

46 Pages Posted: 9 Mar 2002

See all articles by Yannick Malevergne

Yannick Malevergne

Université Paris I Panthéon-Sorbonne - Laboratoire PRISM

Didier Sornette

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

Date Written: March 7, 2002

Abstract

We investigate the relative information content of six measures of dependence between two random variables X and Y for large or extreme events for several models of interest for financial time series. The six measures of dependence are respectively the linear correlation and Spearman's rho conditioned on signed exceedance of one variable above the threshold, or on both variables, the linear correlation conditioned on absolute value exceedance (or large volatility) of one variable, the so-called asymptotic tail-dependence and a probability-weighted tail dependence coefficient. The models are the bivariate Gaussian distribution, the bivariate Student's distribution, and the factor model for various distributions of the factor. We offer explicit analytical formulas as well as numerical estimations for these six measures of dependence in the limit exploring the extreme tails. This provides a quantitative proof that conditioning on exceedance leads to conditional correlation coefficients that may be very different from the unconditional correlation and gives a straightforward mechanism for fluctuations or changes of correlations, based on fluctuations of volatility or changes of trends. Moreover, these various measures of dependence exhibit different and sometimes opposite behaviors, suggesting that, somewhat similarly to risks whose adequate characterization requires an extension beyond the restricted one-dimensional measure in terms of the variance (volatility) to include all higher order cumulants or more generally the knowledge of the full distribution, tail-dependence has also a multidimensional character.

JEL Classification: C10, G10, G15

Suggested Citation

Malevergne, Yannick and Sornette, Didier, Investigating Extreme Dependences: Concepts and Tools (March 7, 2002). Available at SSRN: https://ssrn.com/abstract=303465 or http://dx.doi.org/10.2139/ssrn.303465

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

Didier Sornette (Contact Author)

Risks-X, Southern University of Science and Technology (SUSTech) ( email )

1088 Xueyuan Avenue
Shenzhen, Guangdong 518055
China

Swiss Finance Institute ( email )

c/o University of Geneva
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Switzerland

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

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

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Tokyo Institute of Technology ( email )

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Tokyo 152-8550, 52-8552
Japan