DOI: 10.11908/j.issn.0253-374x.19312

作者:

作者单位: 同济大学 数学科学学院， 上海 200092


作者简介: 梁 进（1958—)，女，教授，博士生导师，理学博士，主要研究方向为信用衍生产品。


通讯作者: 包俊利（1994—)，男，硕士生，主要研究方向为含信用风险的债券。 E-mail: 747649818@qq.com

中图分类号: TP273


基金项目: 国家自然科学基金(11671301)




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

Affiliation: School of Mathematical Sciences, Tongji University, Shanghai 200092, China


Fund Project:




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摘要: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。



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.





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