Pricing of a Perpetual Convertible Bond with Credit Rating Migration Based on Structure Framework

Abstract:

In this paper, the pricing of a two-asset corporate bond with consideration of credit rating migration risks is studied. By using Merton’s structure approach to pricing corporate bond with default risk and giving two kinds of conditions at rating migration, two models for pricing the corporate bond are derived, which can be turned to two-dimensional parabolic equation systems coupled at the rating migration boundary. Besides, the existence and uniqueness of the solution for the model are verified. Moreover, an analytical solution and a numerical solution for the two models are obtained respectively. Furthermore, the effect of credit rating migration on pricing of corporate bond is analyzed and the difference of the two models is compared.