Flexible quadrant copulas: Application to sovereign credit default swaps

Abstract

Abstract

We propose a bivariate quadrant copula built on two contributions. First, we partition the unit square at estimated thresholds and fit a distinct elementary copula in each of the four resulting quadrants, so that within-quadrant dependence may differ in family, in strength and in sign across quadrants, whereas global, asymmetric and mixture copulas tie it to a common parameter vector. Second, we introduce cross-quadrant dependence, estimating the probability of each joint state rather than fixing it, so that total dependence combines a within-quadrant and a cross-quadrant component. Independence across quadrants is the special case in which the second component vanishes, and the model nests it as a restriction that can be tested rather than assumed. We derive the copula, its conditional distributions, rank correlations and tail-dependence coefficients in closed form, and estimate the model by maximum likelihood. An application to sovereign Credit Default Swap spreads shows that the proposed copula outperforms the benchmarks for most country pairs, and identifies the exception as globally coupled.