Utility Indifference Valuation for aDefaultable Corporate Bond with Credit Rating Migration

Mathematics

Zhenghui Li¹  Zhehao Huang¹  Zhenzhen Wang² 

[1] Guangzhou Institute of International Finance, Guangzhou University, Guangzhou 510405, China;School of Mathematics, Sun Yat-sen University, Guangzhou 510275, China;

关键词: utility indifference valuation;    defaultable corporate bond;    credit rating migration;    structural model;    dynamic programming;   

DOI  :  10.3390/math8112033

来源: DOAJ

【 摘 要 】

Credit risk modeling by debt pricing has been a popular theme in both academia and practice since the subprime crisis. In this paper, we devote our study to the indifferent price of a corporate bond with credit risk involving both default risk and credit rating migration risk in an incomplete market. The firm’s stock and a financial index on the market as tradable assets are introduced to hedge the credit risk, and the bond price is determined by the indifference of investors’ utilities with and without holding the bond. The models are established under the structural framework and result in Hamilton–Jacobi–Bellman (HJB) systems regarding utilities subject to default boundary and multiple migration boundaries. According to dynamic programming theory, closed-form solutions for pricing formulas are derived by implementing an inverted iteration program to overcome the joint effect of default and multiple credit rating migration. Therefore, with the derived explicit pricing formulas for the corporate bond, the models can be easily applied in practice, and investors can generate their strategies of hedging the credit risk by easily analyzing the impacts of the parameters on the bond price.

【 授权许可】

Unknown