Shape-based scenario generation using copulas

4 The purpose of this article is to show how the multivariate structure (the ”shape” of the dis5 tribution) can be separated from the marginal distributions when generating scenarios. To do 6 this we use the copula. As a result, we can define combined approaches that capture shape with 7 one method and handle margins with another. In some cases the combined approach is exact, in 8 other cases, the result is an approximation. This new approach is particularly useful if the shape 9 is somewhat peculiar, and substantially different from the standard normal elliptic shape. But it 10 can also be used to obtain the shape of the normal but with margins from different distribution 11 families, or normal margins with for example tail dependence in the multivariate structure. We 12 provide an example from portfolio management. 13