IDEAS home Printed from https://ideas.repec.org/p/arx/papers/1709.06517.html
   My bibliography  Save this paper

Numerical analysis for a unified 2 factor model of structural and reduced form types for corporate bonds with fixed discrete coupon

Author

Listed:
  • Hyong-Chol O.
  • Jong-Chol Kim
  • Il-Gwang Jon

Abstract

Conditions of Stability for explicit finite difference scheme and some results of numerical analysis for a unified 2 factor model of structural and reduced form types for corporate bonds with fixed discrete coupon are provided. It seems to be difficult to get solution formula for PDE model which generalizes Agliardi's structural model [1] for discrete coupon bonds into a unified 2 factor model of structural and reduced form types and we study a numerical analysis for it by explicit finite difference scheme. These equations are parabolic equations with 3 variables and they include mixed derivatives, so the explicit finite difference scheme is not stable in general. We find conditions for the explicit finite difference scheme to be stable, in the case that it is stable, numerically compute the price of the bond and analyze its credit spread and duration.

Suggested Citation

  • Hyong-Chol O. & Jong-Chol Kim & Il-Gwang Jon, 2017. "Numerical analysis for a unified 2 factor model of structural and reduced form types for corporate bonds with fixed discrete coupon," Papers 1709.06517, arXiv.org, revised Aug 2018.
    • Handle: RePEc:arx:papers:1709.06517
    as

    Download full text from publisher

    File URL: http://arxiv.org/pdf/1709.06517
    File Function: Latest version
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Jarrow, Robert A. & Turnbull, Stuart M., 2000. "The intersection of market and credit risk," Journal of Banking & Finance, Elsevier, vol. 24(1-2), pages 271-299, January.
    2. Ballestra, Luca Vincenzo & Pacelli, Graziella, 2014. "Valuing risky debt: A new model combining structural information with the reduced-form approach," Insurance: Mathematics and Economics, Elsevier, vol. 55(C), pages 261-271.
    3. Hyong-Chol O & Yong-Gon Kim & Dong-Hyok Kim, 2013. "Higher Order Binaries with Time Dependent Coefficients and Two Factors - Model for Defaultable Bond with Discrete Default Information," Papers 1305.6868, arXiv.org, revised Jun 2013.
    4. Hyong-Chol O & Dong-Hyok Kim & Jong-Jun Jo & Song-Hun Ri, 2013. "Integrals of Higher Binary Options and Defaultable Bond with Discrete Default Information," Papers 1305.6988, arXiv.org, revised Oct 2013.
    5. 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.
    6. Duffie, Darrell & Singleton, Kenneth J, 1999. "Modeling Term Structures of Defaultable Bonds," The Review of Financial Studies, Society for Financial Studies, vol. 12(4), pages 687-720.
    7. 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..
    8. Lara Cathcart & Lina El-Jahel, 2006. "Pricing defaultable bonds: a middle-way approach between structural and reduced-form models," Quantitative Finance, Taylor & Francis Journals, vol. 6(3), pages 243-253.
    9. 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..
    10. 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.
    11. Rossella Agliardi, 2011. "A comprehensive structural model for defaultable fixed-income bonds," Quantitative Finance, Taylor & Francis Journals, vol. 11(5), pages 749-762.
    12. Hyong-Chol O & Ji-Sok Kim, 2013. "General Properties of Solutions to Inhomogeneous Black-Scholes Equations with Discontinuous Maturity Payoffs and Application," Papers 1309.6505, arXiv.org, revised Sep 2013.
    13. Luca Vincenzo Ballestra & Graziella Pacelli, 2009. "A Numerical Method to Price Defaultable Bonds Based on the Madan and Unal Credit Risk Model," Applied Mathematical Finance, Taylor & Francis Journals, vol. 16(1), pages 17-36.
    14. Geske, Robert, 1977. "The Valuation of Corporate Liabilities as Compound Options," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 12(4), pages 541-552, November.
    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. Hyong Chol O & Tae Song Kim, 2020. "Analysis on the Pricing model for a Discrete Coupon Bond with Early redemption provision by the Structural Approach," Papers 2007.01511, arXiv.org.
    2. 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.
    3. 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.
    4. Hamerle, Alfred & Liebig, Thilo & Rösch, Daniel, 2003. "Credit Risk Factor Modeling and the Basel II IRB Approach," Discussion Paper Series 2: Banking and Financial Studies 2003,02, Deutsche Bundesbank.
    5. Kwamie Dunbar, 2008. "US corporate default swap valuation: the market liquidity hypothesis and autonomous credit risk," Quantitative Finance, Taylor & Francis Journals, vol. 8(3), pages 321-334.
    6. 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.
    7. Giesecke, Kay & Longstaff, Francis A. & Schaefer, Stephen & Strebulaev, Ilya, 2011. "Corporate bond default risk: A 150-year perspective," Journal of Financial Economics, Elsevier, vol. 102(2), pages 233-250.
    8. Tsung-Kang Chen & Hsien-Hsing Liao & Chia-Wu Lu, 2011. "A flow-based corporate credit model," Review of Quantitative Finance and Accounting, Springer, vol. 36(4), pages 517-532, May.
    9. Duffie, Darrell, 2005. "Credit risk modeling with affine processes," Journal of Banking & Finance, Elsevier, vol. 29(11), pages 2751-2802, November.
    10. International Association of Deposit Insurers, 2011. "Evaluation of Deposit Insurance Fund Sufficiency on the Basis of Risk Analysis," IADI Research Papers 11-11, International Association of Deposit Insurers.
    11. Roberto Blanco & Simon Brennan & Ian W Marsh, 2004. "An empirical analysis of the dynamic relationship between investment-grade bonds and credit default swaps," Bank of England working papers 211, Bank of England.
    12. Jose Giancarlo Gasha & Mr. Andre O Santos & Mr. Jorge A Chan-Lau & Mr. Carlos I. Medeiros & Mr. Marcos R Souto & Christian Capuano, 2009. "Recent Advances in Credit Risk Modeling," IMF Working Papers 2009/162, International Monetary Fund.
    13. 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.
    14. Gatzert, Nadine & Martin, Michael, 2012. "Quantifying credit and market risk under Solvency II: Standard approach versus internal model," Insurance: Mathematics and Economics, Elsevier, vol. 51(3), pages 649-666.
    15. 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.
    16. repec:wyi:journl:002109 is not listed on IDEAS
    17. Finbarr Murphy & Bernard Murphy, 2012. "A vector-autoregression analysis of credit and liquidity factor dynamics in US LIBOR and Euribor swap markets," Journal of Economics and Finance, Springer;Academy of Economics and Finance, vol. 36(2), pages 351-370, April.
    18. Leonard Tchuindjo, 2007. "Pricing of Multi-Defaultable Bonds with a Two-Correlated-Factor Hull-White Model," Applied Mathematical Finance, Taylor & Francis Journals, vol. 14(1), pages 19-39.
    19. 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.
    20. 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.
    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:1709.06517. 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.