Asymptotic behaviors of a free boundary raised from corporate bond evaluation with credit rating migration risks

Abstract

In this paper, we study asymptotic behaviors of a free boundary raised from the evaluation of a corporate bond subject to credit rating changes of the underlying company. The credit rating migration is modeled by a free boundary which separates different credit rating regions in a state space. We first formulate the mathematical problem and then establish the well-posedness of the problem and the long time-to-expiry behavior of the solution. As a result, we describe the location and asymptotic line of the free boundary. We also provide certain numerical simulations.