Copulas are an innovative tool in finance to separate marginal distributions, for example of single asset returns, from their dependence structure in modelling multivariate distributions. In principle this allows for the whole variety of univariate distributions that have been developed and introduced into finance in recent years, for example, heavy-tailed distributions, to be used as marginals. Merging the marginals and describing co-movements is left to the copula. Dependence structures expressed by copulas are not fully determined by linear correlation, as is the case with the multivariate normal distribution. Some classes of copulas additionally allow for capturing so-called tail dependence, describing, such as co-movements of asset returns conditional on one being (extremely) negative or positive. With this feature, copulas extend the notion of multivariate normals that is widely used for multi-dimensions, yet the complexity regarding parameters needed to describe certain copulas does not increase proportionately.
February 12, 2001