IDEAS home Printed from https://ideas.repec.org/p/arx/papers/2301.10898.html
   My bibliography  Save this paper

Double free boundary problem for defaultable corporate bond with credit rating migration risks and their asymptotic behaviors

Author

Listed:
  • Yuchao Dong
  • Jin Liang
  • Claude-Michel Brauner

Abstract

In this work, a pricing model for a defaultable corporate bond with credit rating migration risk is established. The model turns out to be a free boundary problem with two free boundaries. The latter are the level sets of the solution but of different kinds. One is from the discontinuous second order term, the other from the obstacle. Existence, uniqueness, and regularity of the solution are obtained. We also prove that two free boundaries are $C^\infty$. The asymptotic behavior of the solution is also considered: we show that it converges to a traveling wave solution when time goes to infinity. Moreover, numerical results are presented.

Suggested Citation

  • Yuchao Dong & Jin Liang & Claude-Michel Brauner, 2023. "Double free boundary problem for defaultable corporate bond with credit rating migration risks and their asymptotic behaviors," Papers 2301.10898, arXiv.org, revised Jul 2023.
    • Handle: RePEc:arx:papers:2301.10898
    as

    Download full text from publisher

    File URL: http://arxiv.org/pdf/2301.10898
    File Function: Latest version
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Robert A. Jarrow & David Lando & Stuart M. Turnbull, 2008. "A Markov Model for the Term Structure of Credit Risk Spreads," World Scientific Book Chapters, in: Financial Derivatives Pricing Selected Works of Robert Jarrow, chapter 18, pages 411-453, World Scientific Publishing Co. Pte. Ltd..
    2. Leland, Hayne E, 1994. "Corporate Debt Value, Bond Covenants, and Optimal Capital Structure," Journal of Finance, American Finance Association, vol. 49(4), pages 1213-1252, September.
    3. Dai, Min & Huang, Shan & Keppo, Jussi, 2019. "Opaque bank assets and optimal equity capital," Journal of Economic Dynamics and Control, Elsevier, vol. 100(C), pages 369-394.
    4. Robert A. Jarrow & Stuart M. Turnbull, 2008. "Pricing Derivatives on Financial Securities Subject to Credit Risk," World Scientific Book Chapters, in: Financial Derivatives Pricing Selected Works of Robert Jarrow, chapter 17, pages 377-409, World Scientific Publishing Co. Pte. Ltd..
    5. Leland, Hayne E & Toft, Klaus Bjerre, 1996. "Optimal Capital Structure, Endogenous Bankruptcy, and the Term Structure of Credit Spreads," Journal of Finance, American Finance Association, vol. 51(3), pages 987-1019, July.
    6. Longstaff, Francis A & Schwartz, Eduardo S, 1995. "A Simple Approach to Valuing Risky Fixed and Floating Rate Debt," Journal of Finance, American Finance Association, vol. 50(3), pages 789-819, July.
    7. Avinash K. Dixit & Robert S. Pindyck, 1994. "Investment under Uncertainty," Economics Books, Princeton University Press, edition 1, number 5474.
    8. Merton, Robert C, 1974. "On the Pricing of Corporate Debt: The Risk Structure of Interest Rates," Journal of Finance, American Finance Association, vol. 29(2), pages 449-470, May.
    9. Briys, Eric & de Varenne, François, 1997. "Valuing Risky Fixed Rate Debt: An Extension," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 32(2), pages 239-248, June.
    10. Black, Fischer & Cox, John C, 1976. "Valuing Corporate Securities: Some Effects of Bond Indenture Provisions," Journal of Finance, American Finance Association, vol. 31(2), pages 351-367, May.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Augusto Castillo, 2004. "Firm and Corporate Bond Valuation: A Simulation Dynamic Programming Approach," Latin American Journal of Economics-formerly Cuadernos de Economía, Instituto de Economía. Pontificia Universidad Católica de Chile., vol. 41(124), pages 345-360.
    2. Suresh M. Sundaresan, 2000. "Continuous‐Time Methods in Finance: A Review and an Assessment," Journal of Finance, American Finance Association, vol. 55(4), pages 1569-1622, August.
    3. Zhehao Huang & Zhenghui Li & Zhenzhen Wang, 2020. "Utility Indifference Valuation for Defaultable Corporate Bond with Credit Rating Migration," Mathematics, MDPI, vol. 8(11), pages 1-26, November.
    4. Martin Dòzsa & Karel Janda, 2015. "Corporate asset pricing models and debt contracts," CAMA Working Papers 2015-33, Centre for Applied Macroeconomic Analysis, Crawford School of Public Policy, The Australian National University.
    5. repec:wyi:journl:002109 is not listed on IDEAS
    6. Viral V. Acharya & Jennifer N. Carpenter, 2002. "Corporate Bond Valuation and Hedging with Stochastic Interest Rates and Endogenous Bankruptcy," The Review of Financial Studies, Society for Financial Studies, vol. 15(5), pages 1355-1383.
    7. Liang, Jin & Zhao, Yuejuan & Zhang, Xudan, 2016. "Utility indifference valuation of corporate bond with credit rating migration by structure approach," Economic Modelling, Elsevier, vol. 54(C), pages 339-346.
    8. Hong-Ming Yin & Jin Liang & Yuan Wu, 2018. "On a New Corporate Bond Pricing Model with Potential Credit Rating Change and Stochastic Interest Rate," JRFM, MDPI, vol. 11(4), pages 1-12, December.
    9. Duffie, Darrell, 2005. "Credit risk modeling with affine processes," Journal of Banking & Finance, Elsevier, vol. 29(11), pages 2751-2802, November.
    10. Samuel Chege Maina, 2011. "Credit Risk Modelling in Markovian HJM Term Structure Class of Models with Stochastic Volatility," PhD Thesis, Finance Discipline Group, UTS Business School, University of Technology, Sydney, number 1-2011.
    11. Moraux, Franck, 2004. "Modeling the business risk of financially weakened firms: A new approach for corporate bond pricing," International Review of Financial Analysis, Elsevier, vol. 13(1), pages 47-61.
    12. Nystrom, Kaj & Skoglund, Jimmy, 2006. "A credit risk model for large dimensional portfolios with application to economic capital," Journal of Banking & Finance, Elsevier, vol. 30(8), pages 2163-2197, August.
    13. Bhanot, Karan & Mello, Antonio S., 2006. "Should corporate debt include a rating trigger?," Journal of Financial Economics, Elsevier, vol. 79(1), pages 69-98, January.
    14. Lie-Jane Kao & Po-Cheng Wu & Tai-Yuan Chen, 2012. "Why Do Banks Default When Asset Quality Is High?," The International Journal of Business and Finance Research, The Institute for Business and Finance Research, vol. 6(1), pages 83-96.
    15. Qiang Dai & Kenneth Singleton, 2003. "Term Structure Dynamics in Theory and Reality," The Review of Financial Studies, Society for Financial Studies, vol. 16(3), pages 631-678, July.
    16. Antonio Trujillo-Ponce & Reyes Samaniego-Medina & Clara Cardone-Riportella, 2014. "Examining what best explains corporate credit risk: accounting-based versus market-based models," Journal of Business Economics and Management, Taylor & Francis Journals, vol. 15(2), pages 253-276, April.
    17. Zhou Lu & Zhuyao Zhuo, 2021. "Modelling of Chinese corporate bond default – A machine learning approach," Accounting and Finance, Accounting and Finance Association of Australia and New Zealand, vol. 61(5), pages 6147-6191, December.
    18. Samuel Chege Maina, 2011. "Credit Risk Modelling in Markovian HJM Term Structure Class of Models with Stochastic Volatility," PhD Thesis, Finance Discipline Group, UTS Business School, University of Technology, Sydney, number 5, July-Dece.
    19. Ming Fang & Rui Zhong, 2004. "Default Risk, Firm's Characteristics, and Risk Shifting," Yale School of Management Working Papers amz2461, Yale School of Management, revised 01 Mar 2005.
    20. Gregory Connor & Lisa R. Goldberg & Robert A. Korajczyk, 2010. "Portfolio Risk Analysis," Economics Books, Princeton University Press, edition 1, number 9224.
    21. Ming Fang & Rui Zhong, 2004. "Default Risk, Firm's Characteristics, and Risk Shifting," Yale School of Management Working Papers amz2461, Yale School of Management, revised 01 Mar 2005.

    More about this item

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:arx:papers:2301.10898. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: arXiv administrators (email available below). General contact details of provider: http://arxiv.org/ .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.