Continuous Displacement Interpolation Between Checkerboard Copulas

This paper presents a displacement-like interpolation method between any two given checkerboard copulas. This interpolation is close to the geodesic connecting the two checkerboard copulas in the L 2-Wasserstein space, which, however, leaves the copula domain. In the proposed interpolation, mass is continuously shifted only across the boundaries of neighboring cells and copula property is ensured at each step. The method therefore can be interpreted as a discrete form of dynamical optimal transport constrained to the copula domain. We illustrate the interpolation with both a toy and a practical example, showing how the method yields dependence structures between two known states.