ETH, Zurich - Department of Mathematics
Although the subject of copulas has a history going back to the 1950s, it is now enjoying a period of fashionability and much of this can be explained by new applications for the theory in the modelling of multivariate financial time series. Copulas are a useful tool for building multivariate distributions with interesting "dependence structures" and, in particular, dependence structures that differ markedly from that of the multivariate normal distribution, which is still widely used in financial applications. Some copula models have the property of tail dependence, which means they have a tendency to generate many joint extreme events; the Gaussian copula (multivariate normal dependence structure) does not have this property. Since extreme movements of stocks or other financial risk factors often occur together it is of interest to see whether we can model this using non-Gaussian copulas, such as the multivariate t copula.
In this talk we review the theories of copulas and tail dependence and we also look at practical statistical aspects of fitting copula models to financial data.