A free boundary problem for defaultable corporate bond with credit rating migration risk and its asymptotic behavior

Yuan Wu; Jin Liang; Bei Hu

doi:10.3934/dcdsb.2019207

Article Contents

2020, Volume 25, Issue 3: 1043-1058. Doi: 10.3934/dcdsb.2019207

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A free boundary problem for defaultable corporate bond with credit rating migration risk and its asymptotic behavior

Yuan Wu^1,,
Jin Liang^2, , and
Bei Hu^3,

1.
School of Statistics and Mathematics, Shanghai Lixin University of Accounting and Finance, Shanghai 201209, China
2.
School of Mathematical Science, Tongji University, Shanghai 200092, China
3.
Department of Applied Computational Mathematics and Statistics, University of Notre Dame, Notre Dame, IN 46556, USA

^* Corresponding author: Jin Liang
^* Corresponding author: Jin Liang

Received: August 2018

Early access: September 2019

Published: March 2020

The second author is supported by National Natural Science Foundation of China (No. 11671301)

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Abstract

In this paper, valuation of a defaultable corporate bond with credit rating migration risk is considered under the structure framework by using a free boundary model. The existence, uniqueness and regularity of the solution are obtained. Furthermore, we analyze the solution's asymptotic behavior and prove that the solution is convergent to an closed form solution. In addition, numerical examples are also shown.

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Mathematics Subject Classification: Primary: 35R35, 35K10; Secondary: 35Q91.

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Figure 1. value function $ \psi(x, t) $

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Figure 2. free boundary

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Figure 3. asymptotic behavior

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