Tail Risk, Systemic Risk and Copulas

Copulas are an elegant mathematical tool for decoupling a joint distribution into the marginal component and the dependence structure component; thus enabling us to model simultaneous events with a greater degree of flexibility. However, as with many statistical techniques, the application of copulas in practice is as much art as it is science. And risk management considerations, such as the increased focus on tail events over central moments, should drive selections of copulas just as much as statistical goodness-of-fit analysis. This paper focuses on several modeling considerations when working with copulas from the perspective of adequately accounting for the behavior in the extreme tails of both the marginal and joint distributions.

Keywords: Copulas; tail risk; systemic risk; joint loss distributions.