Modelling multiple term structures of defaultable bonds with common and idiosyncratic state variables

In this paper we develop a multi-factor “reduced-form” model that is general enough to capture simultaneously the dynamics of multiple term structures of corporate bonds, each with a different credit rating. In this way, we are able to fully incorporate a number of “stylised facts”, reported on a number of previous empirical studies. More specifically, we are able to estimate the different degrees of covariation between the term structure of each credit rating and the default-free yield curve. Furthermore, we report the differing sensitivities of the credit curves to a number of observable macro-factors that reflect changes in credit conditions, both domestic and international. Finally, the dependence of each credit curve on a number of idiosyncratic state-variables is also documented. Our results are based on two special cases of the model, estimated using US and UK corporate bond data.