ABSTRACT
The generation of multivariate probability distributions follows several approaches. Within financial applications the emphasis has mostly been on two methodologies. The first is the elliptical methodology, where the leap from univariate to multivariate has taken place by constructing density functions that are functions of quadratic forms of the marginals. The second is the copula philosophy, where the dependency structure is treated entirely separately from marginals. In financial applications one often needs to work with combinations of marginals of various distributional types, and the copula philosophy is very attractive as it copes well with heterogeneous marginals. However, with some notable exceptions, the copula approach does not normally correspond to any natural or canonical multivariate structure arising from some underlying dynamic.
