A Natural Copula

Copulas are widely used in financial economics, as well as in other areas of applied mathematics. Yet, there is much arbitrariness in their choice. The author proposes a “natural copula” concept that minimizes the Wasserstein distance between distributions in a space in which both distributions are embedded. Transport properties and hydrodynamic interpretation are discussed with two examples of distributions of financial significance. In 2D, a natural copula can be parsimoniously estimated by linear programming methods. A discussion of the construction of multivariate copulas follows. Finally, the quality of the multivariate copula approximation is investigated using the Kolmogorov–Arnold neural network (KAN).