On recovery and intensity's correlation: a new class of credit risk models

Abstract

There has been increasing support in the empirical literature that both the probability of default (PD) and the loss given default (LGD) are correlated and driven by macroeconomic variables. Paradoxically, there has been very little effort from the theoretical literature to develop credit risk models that would include this possibility. The goals of this paper are: first, to develop the theoretical reduced-form framework needed to handle stochastic correlation of recovery and intensity, proposing a new class of models; and, second, to use concrete instance of our class to study the impact of this correlation in credit risk term structures. Our class of models is able to replicate and explain empirically observed features. For instance, we automatically get that periods of economic depression are periods of higher default intensity and where low recovery is more likely - the well-know credit risk business cycle effect. Finally, we show how to calibrate this class of models to market data, and illustrate the technique using our concrete instance using US market data on corporate yields.