Copulae and tail dependence

Abstract

This thesis presents the concept of tail dependence in a financial context as one tool to measure dependence in the extremes of a bivariate distribution. Copulae can separate the problem of estimating a multidimensional distribution into the estimation of the marginal distributions and the dependence between the onedimensional random variables. Therefore, copulae are used in order to carry out the estimation of the tail dependence coefficient (TDC). Four estimators of the TDC are presented and compared in a simulation study for various distributions and copulae. Furthermore, an introduction into bivariate Extreme Value Theory (EVT) is given, which tries precisely to analyze the behavior at the tail of a bivariate distribution. EVT allows to construct estimators of the TDC and to derive a test for tail independence, which is recognized to be indispensable but rarely utilized in a financial context. As an application to nine different financial data sets shows, the phenomenon of tail dependence is less common than often argued in the literature: the periods where indeed tail independence can be rejected are few.