On the Dependence Between Default Risk and Recovery Rates in Structural Models

We define several concepts of dependence between default risk and recovery risk, in a factor model framework. These concepts are illustrated and compared from the perspective of structural models: Merton (1974)’s single horizon and single firm model, multi-factor extensions, possibly under a portfolio approach. Some first-passage time models are discussed too: Kou’s (2002) model and some of its extensions, in particular by adding self-exciting features. We evaluate the different concepts of “default/recovery” dependencies analytically when it is possible, otherwise by simulation.