Communications in Mathematical Sciences

Volume 17 (2019)

Number 7

Asymptotic traveling wave for a pricing model with multiple credit rating migration risk

Pages: 1975 – 2004

DOI: https://dx.doi.org/10.4310/CMS.2019.v17.n7.a9

Authors

Zhenzhen Wang (School of Mathematics, Sun Yat-Sen University, Guangzhou, China)

Zhengrong Liu (School of Mathematics, South China University of Technology, Guangzhou, China)

Tianpei Jiang (School of Information Science and Technology, Shanghai Tech University, Shanghai, China)

Zhehao Huang (Guangzhou International Institute of Finance, Guangzhou University, Guangzhou, China)

Abstract

In this paper, an asymptotic traveling wave of a free boundary problem related to a pricing model for corporate bond with multiple credit rating migration risk is studied. The pricing model is captured by a free boundary problem, whose existence, uniqueness and regularity of the solution are obtained such that the rationality of the model is guaranteed. The existence of a unique traveling wave in the free boundary problem is established with some risk discount rate condition satisfied. The inductive method is applied to overcome the multiplicity of free boundaries. We prove that the solution of the pricing model for corporate bond is convergent to the traveling wave, which shows a clear dynamics of price change for the corporate bond.

Keywords

traveling wave, asymptotic behavior, free boundary problem, multiple credit rating migration, pricing model for corporate bond

2010 Mathematics Subject Classification

35K10, 60H10, 91G40

Received 22 January 2019

Accepted 1 July 2019

Published 6 January 2020