On Portfolio’s Default-Risk-Adjusted Duration and Value: Model and Algorithm Based on Copulas

  • Ping Li
  • Hou-Sheng Chen
  • Guang-Dong Huang
  • Xiao-Jun Shi
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4286)


In this paper, we propose a new approach, copulas, to calculating the default-risk-adjusted duration and present value for a portfolio of bonds vulnerable to default risk. A copula function is used to determine the default dependence structure and simulate correlated default time from individual obligor’s default distribution. This approach is verified to be effective and applicable by a numerical example, in which we demonstrate how to calculate the default-risk-adjusted duration and present value for a given portfolio. In the process we take into account of the settlement time when default happens, the choice of copula function and the correlation between obligors, and make a sensitive analysis of the influence of Kendall’s tau and copula functions on the default-risk-adjusted duration and present value. Results show that the duration and present value simulated from Gaussian copula fluctuates larger than that from Clayton and Gumbel copulas when Kendall’s tau varies from zero to one.


Credit Default Swap Default Risk Default Probability Credit Spread Copula Function 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Bierwag, G.O., Kaufman, G.G.: Durations of non-default-free securities. Financial Analysts Journal 44, 39–46 (1988)CrossRefGoogle Scholar
  2. 2.
    Chance, D.M.: Default risk and the duration of zero coupon bonds. Journal of Finance 45, 265–274 (1990)CrossRefGoogle Scholar
  3. 3.
    Delianedis, G., Geske, R.: Credit risk and risk neutral default probabilities: Information about rating migrations and defaults. The Anderson School, UCLA (1998)Google Scholar
  4. 4.
    Duffie, D., Garleanu, N.: Risk and valuation of collateralized debt obligations. Financial Analyst’s Journal 57, 41–59 (2001)CrossRefGoogle Scholar
  5. 5.
    Embrechets, P., McNeil, A., straumann, D.: Correlation: Pitfalls and Alternatives, Department Mathematik, ETH Zentrum, CH-8092 Zürich, pp. 1–8 (1999)Google Scholar
  6. 6.
    Fooladi, I.J., Roberts, G.S., Skinner, R.: Duration for bonds with default risk. Journal of Banking and Finance 21, 1–16 (1997)CrossRefGoogle Scholar
  7. 7.
    Geske, R.: The valuation of corporate liabilities as compound options. Journal of Financial and Quantitative Analysis 19, 541–552 (1977)CrossRefGoogle Scholar
  8. 8.
    Jacoby, G.: A duration model for defaultable bonds. The journal of financial research 26, 129–146 (2003)CrossRefGoogle Scholar
  9. 9.
    Jonkhart, M.J.L.: On the term structure of interest rates and the risk of default. Journal of Banking and Finance 3, 253–262 (1979)CrossRefGoogle Scholar
  10. 10.
    Lando, D.: On Cox processes and credit risky securities. Review of Derivatives Research 2, 99–120 (1998)Google Scholar
  11. 11.
    Li, D.X.: Constructing a credit curve, Risk, Special report on Credit Risk, 40–44 (November 1998)Google Scholar
  12. 12.
    Li, D.X.: On default correlation: A copula function approach. Journal of Fixed income 9, 43–54 (2000)CrossRefGoogle Scholar
  13. 13.
    Li, P., Chen, H.S.: A Copula Approach to the Pricing of Collateralized Debt Obligation. Lecture Notes in Decision Science (2005)Google Scholar
  14. 14.
    Lucas, D.: Default Correlation and Credit Analysis. Journal of Fixed Income 11, 76–87 (1995)CrossRefMathSciNetGoogle Scholar
  15. 15.
    Meneguzzo, D., Vecchiato, W.: Copula sensitivity in collateralized debt obligation and basket default swaps. The journal of futures Markets 24, 37–70 (2004)CrossRefGoogle Scholar
  16. 16.
    Merton, R.C.: On the pricing of corporate debt: The risk structure of interest rates. Journal of Finance 29, 449–470 (1974)CrossRefGoogle Scholar
  17. 17.
    Nelsen, R.B.: An introduction to copulas. Lecture Notes in Statistics, vol. 139. Springer, New York (1999)zbMATHGoogle Scholar
  18. 18.
    Schönnbucher, P.J., Schubert, D.: Copula-dependent default risk in intensity models, Bonn University. Ecomonics Faculty, Department of Statistics, Working paper (2001)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Ping Li
    • 1
  • Hou-Sheng Chen
    • 1
  • Guang-Dong Huang
    • 2
  • Xiao-Jun Shi
    • 1
  1. 1.School of Economics and ManagementBeihang UniversityBeijingP.R. China
  2. 2.School of Information SciencesChina University of Geosciences (Beijing)BeijingP.R. China

Personalised recommendations