Copula-Models: Theoretical Basis, Empirical Applications and Unresolved Issues

Copula-models enable us to reconstruct multivariate joint distributions given the information on random variables’ marginal distributions and their dependence structure. Several copula families exist (elliptical, Archimedean, extreme and other). There are three principal approaches to copula estimation and generation: parametric, semi-parametric and non-parametric.
Copulas are applied in cases the multivariate joint normality or t-distribution assumption fails. It is the very reason that copula permit us to escape from using the measure of linear correlation in such cases. Copulas are mostly applied to financial problems, e.g. risk estimation, portfolio optimization with respect to risk amount restriction, risk hedging.
Though copula-models are of greater use then those based on joint normality assumption when modeling multivariate joint distribution, certain issues rest to be further researched. Such issues include dealing with large dimensionalities, controlling for the structural break, resolving “one parameter” problem and extending approaches to copula goodness-of-fit testing.