The relationship between two kinds of structural credit migration models

Abstract

In this paper, we presented an asymptotic relationship between the single threshold model and the model with different upgrade and downgrade thresholds for credit migration problems with fixed boundaries. By partial differential equation (PDE) techniques, we proved that the solution of the asymmetric threshold problem converges to that of a single threshold problem uniformly as one of the asymmetric thresholds approaches the other.

Keywords

• credit migration risk
• different upgrade and downgrade thresholds
• asymptotic behavior
• structural model
• corporate bond pricing