A Multi-Credit-Rating Migration Model with Asymmetric Migration Boundaries

Abstract

In this paper, we propose an extended credit migration model with asymmetric fixed boundaries and multiple ratings, for a more precise depiction of credit changes in the real world. A model with three ratings is established and analyzed as an example, and then the results are generalized to a general multirating form model. We prepare the model meaningfully by arranging the asymmetric boundaries in a suitable order. A PDE system problem is deduced, and the existence and uniqueness of the solution for the problem are obtained using PDE techniques, which further ensure the rationality of the model. Due to the flexible configuration of asymmetric boundaries, the multirating model has various types of structures in the buffer zones where the credit rating keeps its original state. For instance, the two buffers in the three-rating model may be separated, connected, or intersected, as presented in the numerical results for different boundary parameters.