IDEAS home Printed from https://ideas.repec.org/a/taf/apfiec/v15y2005i12p875-881.html
   My bibliography  Save this article

Equity and debt valuation with default risk: a discrete structural model

Author

Listed:
  • Marisa Cenci
  • Andrea Gheno

Abstract

Structural models' main source of uncertainty is the stochastic evolution of the firm's asset value. These models are commonly used to value corporate debt at the issue and hence to determine its yield given the amortization plan. This paper proposes two discrete models to value securities issued by a firm which can default before the maturity of its debt either for exogenous or endogenous causes. In either case the equity value is set as the price of a knock-out call option with a discrete monitoring barrier. The first model considers a debt refundable through the payment of known endowments and takes into account that the firm defaults as it fails to meet a promised payment. In the second model the firm's debt is made of a single issue of zero coupon bonds and includes the possibility that the firm defaults prior to the maturity of the debt if its asset value falls below a time dependent barrier. The particular evolution of the asset value, which shows discontinuity in the drift and diffusion coefficient, prevents the use of closed form solutions for options with a discrete monitoring barrier. The evaluation of the option is performed through non-recombining binomial trees.

Suggested Citation

  • Marisa Cenci & Andrea Gheno, 2005. "Equity and debt valuation with default risk: a discrete structural model," Applied Financial Economics, Taylor & Francis Journals, vol. 15(12), pages 875-881.
  • Handle: RePEc:taf:apfiec:v:15:y:2005:i:12:p:875-881
    DOI: 10.1080/09603100500118849
    as

    Download full text from publisher

    File URL: http://www.tandfonline.com/doi/abs/10.1080/09603100500118849
    Download Restriction: Access to full text is restricted to subscribers.

    File URL: https://libkey.io/10.1080/09603100500118849?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. 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.
    2. 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.
    3. Mella-Barral, Pierre & Perraudin, William, 1997. "Strategic Debt Service," Journal of Finance, American Finance Association, vol. 52(2), pages 531-556, June.
    4. 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.
    5. Geske, Robert, 1979. "The valuation of compound options," Journal of Financial Economics, Elsevier, vol. 7(1), pages 63-81, March.
    6. 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.
    7. 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.
    8. 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.
    9. Black, Fischer & Scholes, Myron S, 1973. "The Pricing of Options and Corporate Liabilities," Journal of Political Economy, University of Chicago Press, vol. 81(3), pages 637-654, May-June.
    10. Anderson, Ronald W & Sundaresan, Suresh, 1996. "Design and Valuation of Debt Contracts," The Review of Financial Studies, Society for Financial Studies, vol. 9(1), pages 37-68.
    11. In Joon Kim & Krishna Ramaswamy & Suresh Sundaresan, 1993. "Does Default Risk in Coupons Affect the Valuation of Corporate Bonds?: A Contingent Claims Model," Financial Management, Financial Management Association, vol. 22(3), Fall.
    12. Cox, John C. & Ross, Stephen A. & Rubinstein, Mark, 1979. "Option pricing: A simplified approach," Journal of Financial Economics, Elsevier, vol. 7(3), pages 229-263, September.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Arianna Agosto & Enrico Moretto, 2010. "Applying default probabilities in an exponential barrier structural model," Economics and Quantitative Methods qf1005, Department of Economics, University of Insubria.
    2. Andrea Gheno, 2005. "Corporate valuations and the merton model," Departmental Working Papers of Economics - University 'Roma Tre' 0055, Department of Economics - University Roma Tre.

    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. Abel Elizalde, 2006. "Credit Risk Models II: Structural Models," Working Papers wp2006_0606, CEMFI.
    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. repec:wyi:journl:002109 is not listed on IDEAS
    4. 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.
    5. Correia, Ricardo & Población, Javier, 2015. "A structural model with Explicit Distress," Journal of Banking & Finance, Elsevier, vol. 58(C), pages 112-130.
    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. Dionne, Georges & Laajimi, Sadok, 2012. "On the determinants of the implied default barrier," Journal of Empirical Finance, Elsevier, vol. 19(3), pages 395-408.
    8. Lim, Terence & Lo, Andrew W. & Merton, Robert C. & Scholes, Myron S., 2006. "The Derivatives Sourcebook," Foundations and Trends(R) in Finance, now publishers, vol. 1(5–6), pages 365-572, April.
    9. Duffie, Darrell, 2003. "Intertemporal asset pricing theory," Handbook of the Economics of Finance, in: G.M. Constantinides & M. Harris & R. M. Stulz (ed.), Handbook of the Economics of Finance, edition 1, volume 1, chapter 11, pages 639-742, Elsevier.
    10. Reisz, Alexander S. & Perlich, Claudia, 2007. "A market-based framework for bankruptcy prediction," Journal of Financial Stability, Elsevier, vol. 3(2), pages 85-131, July.
    11. Ericsson, Jan & Jacobs, Kris & Oviedo, Rodolfo, 2009. "The Determinants of Credit Default Swap Premia," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 44(1), pages 109-132, February.
    12. Sheen X. Liu & Howard Qi & Chunchi Wu, 2006. "Personal Taxes, Endogenous Default, and Corporate Bond Yield Spreads," Management Science, INFORMS, vol. 52(6), pages 939-954, June.
    13. Malek Ben-Abdellatif & Hatem Ben-Ameur & Rim Chérif & Bruno Rémillard, 2024. "A two-factor structural model for valuing corporate securities," Review of Derivatives Research, Springer, vol. 27(2), pages 203-225, July.
    14. 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.
    15. Stephanie Heck, 2022. "Corporate bond yields and returns: a survey," Financial Markets and Portfolio Management, Springer;Swiss Society for Financial Market Research, vol. 36(2), pages 179-201, June.
    16. Ayadi, Mohamed A. & Ben-Ameur, Hatem & Fakhfakh, Tarek, 2016. "A dynamic program for valuing corporate securities," European Journal of Operational Research, Elsevier, vol. 249(2), pages 751-770.
    17. Kanak Patel & Ricardo Pereira, 2007. "Expected Default Probabilities in Structural Models: Empirical Evidence," The Journal of Real Estate Finance and Economics, Springer, vol. 34(1), pages 107-133, January.
    18. Batten, Jonathan & Hogan, Warren, 2002. "A perspective on credit derivatives," International Review of Financial Analysis, Elsevier, vol. 11(3), pages 251-278.
    19. Duffie, Darrell, 2005. "Credit risk modeling with affine processes," Journal of Banking & Finance, Elsevier, vol. 29(11), pages 2751-2802, November.
    20. 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, January-A.
    21. Ryoichi Ikeda & Yoske Igarashi, 2016. "Credit risk analysis with creditor’s option to extend maturities," Annals of Finance, Springer, vol. 12(3), pages 275-304, December.

    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:taf:apfiec:v:15:y:2005:i:12:p:875-881. 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: Chris Longhurst (email available below). General contact details of provider: http://www.tandfonline.com/RAFE20 .

    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.