Hostname: page-component-77c89778f8-rkxrd Total loading time: 0 Render date: 2024-07-18T09:27:31.907Z Has data issue: false hasContentIssue false
  • English
  • Français

A Two-Factor Hazard Rate Model for Pricing Risky Debt and the Term Structure of Credit Spreads

Published online by Cambridge University Press:  06 April 2009

Dilip Madan  and
Haluk Unal
Get access Rights & Permissions [Opens in a new window]

Abstract

This paper proposes a two-factor hazard rate model, in closd form, to price risky debt. The likelihood of default is captured by the firm's non-interest sensitive assets and default-free interest rates. The distinguishing features of the model are threefold. First, the impact of capital structure changes on credit spreads can be analyzed. Second, the model allows stochastic interest rates to impact current asset values as well as their evolution. Finally, the proposed model is in closed fom, enabling us to undertake comparative statics analysis, compute parameter deltas of the model, calibrate empirical credit spreads, and determine hedge positions. Credit spreads generated by our model are consistent with empirical observations.

Type
Research Article
Information
Journal of Financial and Quantitative Analysis , Volume 35 , Issue 1 , March 2000 , pp. 43 - 65
Copyright
Copyright © School of Business Administration, University of Washington 2000

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

Footnotes

*

Both authors, Robert H. Smith school of Business, University of Maryland, College Park, MD 20742. The authors are grateful for the detailed comments from Gurdip Bakshi, Chris James, James Moser, Gordon Phillips, Lemma Senbet, Klaus Toft, Alex Triantis, Xiao Peng Zhang, and Sanjiv Das (the referee) as well as seminar paticipants at the University of Maryland, Bank Structure Conference at the Federal Reserve Bank of Chicago, May 1998, and European Finance Association Meetings in Fontainebleau in August 1998, ICBI conference on Global Derivatives, Paris, April 1999, Tenth Annual Conference on Financial Economics and Accounting, University of Texas at Austin, October 1999, Credit Risk Summit, Risk Conference London and New York, October 1999, ICBI Conference on Risk Management Geneva, November 1999, and VIII Tor Vergata Financial Conference, University of Rome, December 1999.

References

Artzner, P., and Delbean, F.. “Default Risk Insurance and Incomplete Markets.” Mathematical Finance, 5 (07 1995), 187–195.10.1111/j.1467-9965.1995.tb00064.xCrossRefGoogle Scholar
Baxter, M., and Rannie, A.. Financial Calculus. Cambridge, England: Cambridge Univ. Press(1966).Google Scholar
Bjork, T. “Interest Rate Theory.” In Financial Mathematics, Bressanone, Lecture Notes in Mathematics 1656. Berlin, Germany: Springer-Verlag (1996), 53–122.Google Scholar
Briys, E., and de Varenne, F.. “Valuing Risky Fixed Debt: An Extension.” Journal of Financial and Quantitative Analysis, 32 (06 1997), 239–248.10.2307/2331175S002210900000082XCrossRefGoogle Scholar
Cox, J. C.; Ingersoll, J. E. Jr; and Ross, S. A.. “A Theory of the Term Structure of Interest Rates.” Econometrica, 53 03 1985), 385–407.10.2307/1911242CrossRefGoogle Scholar
Cooper, I. A., and Mello, A. S.. “The Default Risk of Swaps. Journal of Finance, 47 (06 1992), 597–620.Google Scholar
Das, S. R., and Tufano, P.. “Pricing Credit-sensitive Debt when Interest Rates, Credit Ratings and Credit Spreads are Stochastic.” Journal of Financial Engineering, 5 (06 1996), 161–198.Google Scholar
Duffee, G. R. “Treasury Yields and Corporate Bond Yield Spreads: An Empirical Analysis.” Journal of Finance, 53 (12 1998), 2225–2242.10.1111/0022-1082.00089CrossRefGoogle Scholar
Duffie, D., and Lando, D.. “Term Structure of Credit Spreads with Incomplete Accounting Information.” Working Paper, Stanford Univ.(1997).Google Scholar
Duffie, D., and singleton, K. J.. “An Econometric Model of the Term Structure of Interest Rate Swap Yields.” Journal of Finance, 52 (09 1997), 1287–1323.10.2307/2329437Google Scholar
Duffie, D., and singleton, K. J.. “Modelling Term Structures of Defaultable Bonds.” Review of Financial Studies, 12(1999), 687–720.10.1093/rfs/12.4.687CrossRefGoogle Scholar
Elliott, R. J. Stochastic Calculus and Applications. New York, NY: Springer-Verlag (1982).Google Scholar
Geman, H.; Karoui, N. El; and Rochet, J. C.. “Change of Numeraire, Changes of Probability Measures and Pricing of Options.” Journal of Applied Probability, 32 (1995), 443–458.10.2307/3215299CrossRefGoogle Scholar
Heath, D.; Jarrow, R.; and Morton, A.. “Bond Pricing and the Term Structure of Interest Rates: A New Methodology for Contingent Claims Valuation.” Econometrica, 60 (01 1992), 77–106.10.2307/2951677CrossRefGoogle Scholar
Hull, J., and White, A.. “The Impact of Default Risk on the Prices of Options and Other Drivative Securities.” Journal of? Banking and Finance, 19 (05 1995), 299–322.10.1016/0378-4266(94)00050-DCrossRefGoogle Scholar
Jamshidian, F. “An Exact Bond Option Formula.” Journal of Finance, 44 (03 1989), 205–209.10.2307/2328284CrossRefGoogle Scholar
Jarrow, R. A., and Turnbull, S. M.. “Pricing Derivatives on Financial Securities Subject to Credit Risk.” Journal of Finance, 50 (03 1995), 53–85.10.2307/2329239CrossRefGoogle Scholar
Jarrow, R. A.; Lando, D.; and Turnbull, S. M.. “A markov Model for the Term Structure of Credit Risk Spreads.” Review of Financial Studies, 10 (1997), 481–523.10.1093/rfs/10.2.481CrossRefGoogle Scholar
Jones, E.; Mason, S.; and Rosenfeld, E.. “Contingent Claims Analysis of Corporate Capital Structures: An Empirical Investigation.” Journal of Finance, 39 (07 1984), 611–627.10.2307/2327919CrossRefGoogle Scholar
Kim, J.; Ramaswamy, K.; and Sundareasn, S.. “Does Default Risk in Coupons Affect the Valuation of Corporate Bonds?: A Contingent Claims Model.” Financial Management, 22 (Autumn 1993), 117–131.10.2307/3665932CrossRefGoogle Scholar
Lando, D. “Modelling Bonds and Derivatives with Default risk.” In Mathematics of Derivative Securities, Dempster, M. and Pliska, S., eds. Cambridge, England: Cambridge Univ. Press (1977), 369–393.Google Scholar
Leland, H. “Coroporate Debt Value, Bond Covenants, and Optimal Capital Structure.” Journal of Finance, 49 (09 1994), 1213–1252.10.2307/2329184CrossRefGoogle Scholar
Leland, H. E., and Toft, K. B.. “Optimal Capital Structure, Endogenous Bankruptey, and the Term Structure of Credit Spreads.” Journal of finance, 51 (07 1996), 987–1019.10.2307/2329229Google Scholar
Longstaff, F., and Schwartz, E.. “A Simple Approach to Valuning Risky Fixed and Floating Rate Debt.” Journal of Finance, 50 (09 1995), 789–819.10.2307/2329288CrossRefGoogle Scholar
Madan, D., and Unal, H.. “Pricing the Risks of Default.” Review of Derivatives Research, 2 (1998), 121–160.CrossRefGoogle Scholar
Merton, R. C. “On the Pricing of Corporate Debt: The Risk Structure of Interest Rates.” Jounal of Finance, 29 (05 1974), 449–470.10.2307/2978814Google Scholar
Morris, C.; Neal, R.; and Rolph, D.. “Credit Spreads in Interest Rates: A Cointegration Approach.” Working Paper, Indian Univ. (1998).Google Scholar
Nielsen, S., and Ronn, E.. “The Valuation of Default Risk in Corporte Bonds and Interest Rate Swaps. Working Paper, Univ.of Texas at Austin (1995).Google Scholar
Vasicek, O. “An Equilibrium Characterization of the Term Structure.” Jounal of Financial economics, 5(1997), 177–188.10.1016/0304-405X(77)90016-2CrossRefGoogle Scholar
Zhou, C. S. “A Jump-Diffusion Approach to Modeling Credit Risk and Valuing defaultable Securities.” Working Paper, Federal Reserve Board (1997).Google Scholar