Abstract
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.
This work is supported by the National Natural Science Foundation of China, grant 70501003.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Bierwag, G.O., Kaufman, G.G.: Durations of non-default-free securities. Financial Analysts Journal 44, 39–46 (1988)
Chance, D.M.: Default risk and the duration of zero coupon bonds. Journal of Finance 45, 265–274 (1990)
Delianedis, G., Geske, R.: Credit risk and risk neutral default probabilities: Information about rating migrations and defaults. The Anderson School, UCLA (1998)
Duffie, D., Garleanu, N.: Risk and valuation of collateralized debt obligations. Financial Analyst’s Journal 57, 41–59 (2001)
Embrechets, P., McNeil, A., straumann, D.: Correlation: Pitfalls and Alternatives, Department Mathematik, ETH Zentrum, CH-8092 Zürich, pp. 1–8 (1999)
Fooladi, I.J., Roberts, G.S., Skinner, R.: Duration for bonds with default risk. Journal of Banking and Finance 21, 1–16 (1997)
Geske, R.: The valuation of corporate liabilities as compound options. Journal of Financial and Quantitative Analysis 19, 541–552 (1977)
Jacoby, G.: A duration model for defaultable bonds. The journal of financial research 26, 129–146 (2003)
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)
Lando, D.: On Cox processes and credit risky securities. Review of Derivatives Research 2, 99–120 (1998)
Li, D.X.: Constructing a credit curve, Risk, Special report on Credit Risk, 40–44 (November 1998)
Li, D.X.: On default correlation: A copula function approach. Journal of Fixed income 9, 43–54 (2000)
Li, P., Chen, H.S.: A Copula Approach to the Pricing of Collateralized Debt Obligation. Lecture Notes in Decision Science (2005)
Lucas, D.: Default Correlation and Credit Analysis. Journal of Fixed Income 11, 76–87 (1995)
Meneguzzo, D., Vecchiato, W.: Copula sensitivity in collateralized debt obligation and basket default swaps. The journal of futures Markets 24, 37–70 (2004)
Merton, R.C.: On the pricing of corporate debt: The risk structure of interest rates. Journal of Finance 29, 449–470 (1974)
Nelsen, R.B.: An introduction to copulas. Lecture Notes in Statistics, vol. 139. Springer, New York (1999)
Schönnbucher, P.J., Schubert, D.: Copula-dependent default risk in intensity models, Bonn University. Ecomonics Faculty, Department of Statistics, Working paper (2001)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2006 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Li, P., Chen, HS., Huang, GD., Shi, XJ. (2006). On Portfolio’s Default-Risk-Adjusted Duration and Value: Model and Algorithm Based on Copulas. In: Spirakis, P., Mavronicolas, M., Kontogiannis, S. (eds) Internet and Network Economics. WINE 2006. Lecture Notes in Computer Science, vol 4286. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11944874_20
Download citation
DOI: https://doi.org/10.1007/11944874_20
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-68138-0
Online ISBN: 978-3-540-68141-0
eBook Packages: Computer ScienceComputer Science (R0)