Invariance Properties in the Dynamic Gaussian Copula Model*

Abstract

Based on Gaussian tail distribution estimates of independent interest, we study the mathematical properties of the default times (or any of their minima) in the dynamic Gaussian copula model. In particular, depending on the value of the correlation parameter ϱ in the model, the so-called invariance property of CrepeySong15c may be satisfied or not. This gives together an example of a model where the invariance property is satisfied but immersion does not hold, for small ϱ and, for larger ϱ an example of a model where the invariance property may not be satisfied.

Keywords

• counterparty credit risk
• wrong-way risk
• gaussian copula
• dynamic copula
• immersion property
• invariance time
• cds