ETH, Zurich - Department of Mathematics
We discuss the class of multivariate normal mean-variance mixture distributions, which contains both the multivariate Student t distribution and the generalized hyperbolic distribution. In low-dimensional empirical studies these distributions have been found to provide a reasonable model for daily and weekly stock or exchange rate returns. We present an EM-type algorithm for fitting these models in arbitrary dimensions and discuss our findings in analyses of financial data. We then focus our attention on the dependence structures or copulas of these distributions and discuss to what extent they are able to capture the phenomenon of "dependence in the tail" which is often observed in financial return data, i.e. the tendency for the most extreme returns in one return series to be acccompanied by the most extreme returns in other series. A review of necessary ideas in copula theory and links to the theory of multivariate extremes will be given.