  We prove that the default times (or any of their minima) in the dynamic
Gaussian copula model of Cr{\'e}pey, Jeanblanc, and Wu (2013) are invariance
times in the sense of Cr{\'e}pey 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.
