Richard Koivusalo: Statistical analysis of empirical pairwise copulas for the S & P 500 stocks

It is of great importance to find an analytical copula that will represent the empirical tail dependence. In this study, the pairwise empirical copula is built out of data from S & P 500, during the period 2007 - 2010. Different optimization methods and measures of dependence have been used to fit Gaussian, Student t and Clayton copula to the empirical copula, in order to represent the empirical tail dependence. These different measures of dependence and optimization methods with its restrictions, points at different analytical copulas, being optimal. In this study, Student t with degrees of freedom, \nu=5, is giving the most fulfilling result, when it comes to representing tail dependence. Student t (\nu=5) is best, whether one uses the empirical maximum likelihood estimator, or equal Kendall's \tau as an approach.