Invariance properties in the dynamic gaussian copula model *

Stéphane Crépey (1) , Shiqi Song (1)

1 LaMME - Laboratoire de Mathématiques et Modélisation d'Evry

We prove that the default times (or any of their minima) in the dynamic Gaussian copula model of Crépey, Jeanblanc, and Wu (2013) are invariance times in the sense of Crépey and Song (2017), with related invariance probability measures different from the pricing measure. This reflects a departure from the immersion property, whereby the default intensities of the surviving names and therefore the value of credit protection spike at default times. These properties are in line with the wrong-way risk feature of counterparty risk embedded in credit derivatives, i.e. the adverse dependence between the default risk of a counterparty and an underlying credit derivative exposure.

Mots clés: immersion property; dynamic copula; counterparty credit risk; wrong-way risk; Gaussian copula; invariance; time; CDS

Domaines: Finance quantitative [q-fin.CP]

Stéphane Crépey, Shiqi Song. Invariance properties in the dynamic gaussian copula model *. 2017. ⟨hal-01455424⟩