Shape-based Scenario Generation using Copulas

Abstract

The purpose of this article is to show how the multivariate structure (the ”shape” of the distribution) can be separated from the marginal distributions when generating scenarios. To dothis we use the copula. As a result, we can define combined approaches that capture shape with one method and handle margins with another. In some cases the combined approach is exact, inother cases, the result is an approximation. This new approach is particularly useful if the shape is somewhat peculiar, and substantially different from the standard normal elliptic shape. But it can also be used to obtain the shape of the normal but with margins from different distribution families, or normal margins with for example tail dependence in the multivariate structure. We provide an example from portfolio management.