含信用等级迁移的公司债券基于双资产的结构化定价

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

研究含信用等级迁移风险的公司债券在双资产影响下的定价问题。基于Merton的公司债券结构化定价方法,建立含信用等级迁移风险的公司债券关于流动资产和固定资产的模型假设,分析债券的未来预期收益,给出在信用等级迁移边界处耦合的偏微分方程组,在信用等级迁移边界处添加一阶导数条件或线性组合条件,建立起债券的定价模型。求得了数值解和解析解,最后对模型进行了数值分析。

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.