Orthogonal Grid Constructions of Copulas

We establish a general framework for constructing copulas that can be regarded as a patchwork-like assembly of arbitrary copulas, with nonoverlapping rectangles as patches. We derive a family of construction methods that require the choice of a single background copula. When this background copula is the greatest copula , we retrieve the well-known ordinal sum construction, while in the case of the smallest copula , we obtain a construction method that is dual to the ordinal sum construction. Also nonsingular background copulas lead to suitable construction methods.