Stress-Testing the Impact of Group Dependence on Credit Portfolio Risk

Abstract

systematic factors and the latter are responsible for default dependence between different firms. Another source of default dependence is structural links between firms. For example, a mother company may consist of different legal entities and a default of the former may be contagious and lead to the default of all others, i.e. strong dependence is present in this case. Conversely a possible default from one of the constituent companies may be prevented by the mother company.

In fact, such dependence or guarantee considerations are often made when assessing the individual default probabilities, and then typically result in assigning lower default probabilities to daughter companies.

While it is correct to consider these direct dependence relations when assessing the single default probabilities they also need to be considered when modelling the aggregate loss but it appears that this is ignored by the current state-of-the-art credit risk portfolio models.

In this paper we will use the CreditRisk model to stress-test the direct (intra-)group dependences or contagion effects by making these as strong as possible while leaving the other characteristics of the portfolio unchanged. Then, we show how this model can still be readily applied without major modifications. We also show that the CreditRisk model will allow us to derive the loss distribution function explicitly.

Keywords: Dependence, correlations, credit risk, contagion, group risk, Panjer's recursion