Researchers and practitioners are interested in the associations between variables at extreme values in which large amount of profits or losses in financial industry are considered. Sibuya (1960) proposed a conditional dependence structure, called tail dependence coefficient, to measure the asymptotic dependency between variables. This coefficient has become a standard measurement of associations between variables at extreme values.
In this talk, we propose a functional tail dependence structure between two variables at their extremities in the sense that the rates approaching to extremities are functionally different. We obtain definite solutions of such proposed tail dependence coefficients for six commonly used copulas under mild assumptions. In addition, empirical studies are carried out for financial data.
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