Credit Risk Propagation in Structural-Form Models

Existing empirical studies on correlated defaults have shown that the default of a firm impacts other firms; however, this impact has yet to be theoretically validated and quantified, especially under a structural-form model with more than two firms, and with multiple firms that are all likely to default with almost equal weight. To fill the gap, this paper studies how the firm value processes interact with each other in the presence of correlated defaults as well as a large number of firms. To this end, a new renewal theory is developed. The results show that even under a simple one-factor model, the idiosyncratic moments of the defaulted firm transfer to other firms at the time of default, causing a propagation in credit risk. Furthermore, we can quantify this propagation via asymptotic theory, which provides a multiname distance-to-default type risk measure for a system of firms. The results potentially constitute a new method in studying contagion and other correlated default effects and therefore provide new measurements in credit risk management. Numerical and empirical studies are presented to illustrate our claim.