Modelling the dependence structure of financial assets : A survey of four copulas

Understanding and quantifying dependence is at the core of all modelling efforts in financial econometrics. The linear correlation coefficient, which is the far most used measure to test dependence in the financial community and also elsewhere, is only a measure of linear dependence. This means that it is a meaningful measure of dependence if asset returns are well represented by an elliptical distribution. Outside the world of elliptical distributions, however, using the linear correlation coefficient as a measure of dependence may lead to misleading conclusions. Hence, alternative methods for capturing co-dependency should be considered. One class of alternatives are copula-based dependence measures. In this survey we consider two parametric families of copulas; the copulas of normal mixture distributions and Archimedean copulas.

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