Shaping tail dependencies by nesting box copulas

TL;DR

This paper introduces a new family of copulas that are locally piecewise uniform, allowing for precise control of tail dependencies across all projections, with an efficient sampling method suitable for risk modeling.

Contribution

It presents a novel family of copulas with controllable tail dependencies and an efficient sampling algorithm, enhancing risk modeling capabilities.

Findings

Family of copulas with local piecewise uniformity

Control over tail dependencies of all projections

Efficient sampling algorithm for practical use

Abstract

We introduce a family of copulas which are locally piecewise uniform in the interior of the unit cube of any given dimension. Within that family, the simultaneous control of tail dependencies of all projections to faces of the cube is possible and we give an efficient sampling algorithm. The combination of these two properties may be appealing to risk modellers.