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.
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