Modelling cascading effects for systemic risk: Properties of the Freund copula

Abstract

We consider a dependent lifetime model for systemic risk, whose basic idea was for the first time presented by Freund. This model allows to model cascading effects of defaults for arbitrarily many economic agents. We study in particular the pertaining bivariate copula function. This copula does not have a closed form and does not belong to the class of Archimedean copulas, either.We derive some monotonicity properties of it and show how to use this copula for modelling the cascade effect implicitly contained in observed CDS spreads.

Keywords

• dependent lifetime models
• upper orthant order
• systemic risk
• 60e05
• 62e10