# Invariance properties in the dynamic gaussian copula model *

## TL;DR

This paper demonstrates that in the dynamic Gaussian copula model, default times exhibit invariance properties that relate to wrong-way risk, highlighting a departure from traditional immersion assumptions and impacting credit derivative valuation.

## Contribution

It proves that default times in the dynamic Gaussian copula model are invariance times with measures different from the pricing measure, revealing new insights into wrong-way risk.

## Key findings

- Default times are invariance times with respect to certain probability measures.
- Default intensities spike at default times, indicating departure from immersion property.
- The results align with the wrong-way risk feature in credit derivatives.

## Abstract

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.