Copula Models (Gaussian, t, Clayton, Gumbel, Frank)

Copula models are a family of functions that describe the dependence structure between variables separately from their individual (marginal) distributions. The foundation is Sklar's theorem (1959), which shows that any multivariate distribution can be split into its marginals plus a copula; Joe (1997) developed the modern catalogue of dependence concepts. They are central to portfolio risk and credit modelling.