IDEAS home Printed from https://ideas.repec.org/a/gam/jjrfmx/v9y2016i3p7-d73405.html
   My bibliography  Save this article

Probability of Default and Default Correlations

Author

Listed:
  • Weiping Li

    (Institute of Finance and Big Data, Southwest Jiaotong University, Chengdu 611756, Sichuan, China
    Department of Finance, Oklahoma State University, Stillwater, OK 74078-4011, USA)

Abstract

We consider a system where the asset values of firms are correlated with the default thresholds. We first evaluate the probability of default of a single firm under the correlated assets assumptions. This extends Merton’s probability of default of a single firm under the independent asset values assumption. At any time, the distance-to-default for a single firm is derived in the system, and this distance-to-default should provide a different measure for credit rating with the correlated asset values into consideration. Then we derive a closed formula for the joint default probability and a general closed formula for the default correlation via the correlated multivariate process of the first-passage-time default correlation model. Our structural model encodes the sensitivities of default correlations with respect to the underlying correlation among firms’ asset values. We propose the disparate credit risk management from our result in contrast to the commonly used risk measurement methods considering default correlations into consideration.

Suggested Citation

  • Weiping Li, 2016. "Probability of Default and Default Correlations," JRFM, MDPI, vol. 9(3), pages 1-19, July.
    • Handle: RePEc:gam:jjrfmx:v:9:y:2016:i:3:p:7-:d:73405
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/1911-8074/9/3/7/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/1911-8074/9/3/7/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Philippe Jorion, 2009. "Risk Management Lessons from the Credit Crisis," European Financial Management, European Financial Management Association, vol. 15(5), pages 923-933, November.
    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. 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.
    4. 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.
    5. Zhou, Chunsheng, 2001. "An Analysis of Default Correlations and Multiple Defaults," The Review of Financial Studies, Society for Financial Studies, vol. 14(2), pages 555-576.
    6. Metzler, Adam, 2010. "On the first passage problem for correlated Brownian motion," Statistics & Probability Letters, Elsevier, vol. 80(5-6), pages 277-284, March.
    7. 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.
    8. Giesecke, Kay, 2004. "Correlated default with incomplete information," Journal of Banking & Finance, Elsevier, vol. 28(7), pages 1521-1545, July.
    9. Weiping Li & Tim Krehbiel, 2016. "An Improved Approach To Evaluate Default Probabilities And Default Correlations With Consistency," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 19(05), pages 1-29, August.
    10. 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.
    11. Erlenmaier, Ulrich & Gersbach, Hans, 2001. "Default probabilities and default correlations," Research Notes 01-5, Deutsche Bank Research.
    12. Ulrich Erlenmaier & Hans Gersbach, 2014. "Default Correlations in the Merton Model," Review of Finance, European Finance Association, vol. 18(5), pages 1775-1809.
    13. Crouhy, Michel & Galai, Dan & Mark, Robert, 2000. "A comparative analysis of current credit risk models," Journal of Banking & Finance, Elsevier, vol. 24(1-2), pages 59-117, January.
    14. Jarrow, Robert A., 2011. "Credit market equilibrium theory and evidence: Revisiting the structural versus reduced form credit risk model debate," Finance Research Letters, Elsevier, vol. 8(1), pages 2-7, March.
    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. Philip Protter & Alejandra Quintos, 2021. "Stopping Times Occurring Simultaneously," Papers 2111.09458, arXiv.org, revised Nov 2022.

    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. Weiping Li & Tim Krehbiel, 2016. "An Improved Approach To Evaluate Default Probabilities And Default Correlations With Consistency," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 19(05), pages 1-29, August.
    2. 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.
    3. 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.
    4. Ulrich Erlenmaier & Hans Gersbach, 2014. "Default Correlations in the Merton Model," Review of Finance, European Finance Association, vol. 18(5), pages 1775-1809.
    5. Abel Elizalde, 2006. "Credit Risk Models II: Structural Models," Working Papers wp2006_0606, CEMFI.
    6. Giesecke, Kay, 2006. "Default and information," Journal of Economic Dynamics and Control, Elsevier, vol. 30(11), pages 2281-2303, November.
    7. Zhijian (James) Huang & Yuchen Luo, 2016. "Revisiting Structural Modeling of Credit Risk—Evidence from the Credit Default Swap (CDS) Market," JRFM, MDPI, vol. 9(2), pages 1-20, May.
    8. 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.
    9. 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.
    10. Nan Chen & S. G. Kou, 2009. "Credit Spreads, Optimal Capital Structure, And Implied Volatility With Endogenous Default And Jump Risk," Mathematical Finance, Wiley Blackwell, vol. 19(3), pages 343-378, July.
    11. Dionne, Georges & Laajimi, Sadok, 2012. "On the determinants of the implied default barrier," Journal of Empirical Finance, Elsevier, vol. 19(3), pages 395-408.
    12. 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.
    13. Nakashima, Kiyotaka & Saito, Makoto, 2009. "Credit spreads on corporate bonds and the macroeconomy in Japan," Journal of the Japanese and International Economies, Elsevier, vol. 23(3), pages 309-331, September.
    14. Duffie, Darrell, 2005. "Credit risk modeling with affine processes," Journal of Banking & Finance, Elsevier, vol. 29(11), pages 2751-2802, November.
    15. Jean-David Fermanian, 2020. "On the Dependence between Default Risk and Recovery Rates in Structural Models," Annals of Economics and Statistics, GENES, issue 140, pages 45-82.
    16. 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.
    17. 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.
    18. 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.
    19. 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.
    20. Zhou, Xinghua & Reesor, R. Mark, 2015. "Misrepresentation and capital structure: Quantifying the impact on corporate debt value," Journal of Corporate Finance, Elsevier, vol. 34(C), pages 293-310.

    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:gam:jjrfmx:v:9:y:2016:i:3:p:7-:d:73405. 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: MDPI Indexing Manager (email available below). General contact details of provider: https://www.mdpi.com .

    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.