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The Term Structure of Defaultable Bond Prices

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  • Schönbucher, Philipp J.
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    Abstract

    In this paper we present a new methodology for modelling the development of the prices of defaultable zero coupon bonds that is inspired by the Heath-Jarrow-Morton (HJM) approach to risk-free interest rate modelling. Instead of precisely specifying the mechanism that triggers the default we concentrate on modelling the development of the term structure of the defaultable bonds and give conditions under which these dynamics are arbitrage-free. These conditions are a drift restriction that is closely related to the HJM drift restriction for risk-free bonds, and the restriction that the defaultable short rate must always be not below the risk-free short rate. The same restrictions apply for the extended versions of the model that allow for restructuring of defaulted debt and multiple defaults, and loss quotas that are not predictable. In its most general version the model is set in a marked point process framework, to allow for jumps in the defaultable rates at times of default.

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    File URL: http://www.wiwi.uni-bonn.de/bgsepapers/bonsfb/bonsfb384.pdf
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    Bibliographic Info

    Paper provided by University of Bonn, Germany in its series Discussion Paper Serie B with number 384.

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    Length: pages
    Date of creation: Aug 1996
    Date of revision:
    Handle: RePEc:bon:bonsfb:384

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    Postal: Bonn Graduate School of Economics, University of Bonn, Adenauerallee 24 - 26, 53113 Bonn, Germany
    Fax: +49 228 73 6884
    Web page: http://www.bgse.uni-bonn.de

    Related research

    Keywords: arbitrage; term structure of interest rates; default risk;

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    References

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    1. Merton, Robert C., 1975. "Option pricing when underlying stock returns are discontinuous," Working papers 787-75., Massachusetts Institute of Technology (MIT), Sloan School of Management.
    2. Vasicek, Oldrich, 1977. "An equilibrium characterization of the term structure," Journal of Financial Economics, Elsevier, vol. 5(2), pages 177-188, November.
    3. Hull, John & White, Alan, 1993. "One-Factor Interest-Rate Models and the Valuation of Interest-Rate Derivative Securities," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 28(02), pages 235-254, June.
    4. Cox, John C & Ingersoll, Jonathan E, Jr & Ross, Stephen A, 1985. "An Intertemporal General Equilibrium Model of Asset Prices," Econometrica, Econometric Society, vol. 53(2), pages 363-84, March.
    5. Ho, Thomas S Y & Lee, Sang-bin, 1986. " Term Structure Movements and Pricing Interest Rate Contingent Claims," Journal of Finance, American Finance Association, vol. 41(5), pages 1011-29, December.
    6. Björk, T. & Kabanov, Y. & Runggaldier, W., 1995. "Bond markets where prices are driven by a general marked point process," Working Paper Series in Economics and Finance 88, Stockholm School of Economics.
    7. 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 449-70, May.
    8. 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 637-54, May-June.
    9. Cox, John C & Ingersoll, Jonathan E, Jr & Ross, Stephen A, 1985. "A Theory of the Term Structure of Interest Rates," Econometrica, Econometric Society, vol. 53(2), pages 385-407, March.
    10. Philippe Artzner & Freddy Delbaen, 1995. "Default Risk Insurance And Incomplete Markets," Mathematical Finance, Wiley Blackwell, vol. 5(3), pages 187-195.
    11. Franks, Julian R. & Torous, Walter N., 1994. "A comparison of financial recontracting in distressed exchanges and chapter 11 reorganizations," Journal of Financial Economics, Elsevier, vol. 35(3), pages 349-370, June.
    12. Tomas Björk & Yuri Kabanov & Wolfgang Runggaldier, 1997. "Bond Market Structure in the Presence of Marked Point Processes," Mathematical Finance, Wiley Blackwell, vol. 7(2), pages 211-239.
    13. Heath, David & Jarrow, Robert & Morton, Andrew, 1992. "Bond Pricing and the Term Structure of Interest Rates: A New Methodology for Contingent Claims Valuation," Econometrica, Econometric Society, vol. 60(1), pages 77-105, January.
    14. Geske, Robert, 1977. "The Valuation of Corporate Liabilities as Compound Options," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 12(04), pages 541-552, November.
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    Cited by:
    1. Philipp J. Schönbucher, 2000. "A Tree Implementation of a Credit Spread Model for Credit Derivatives," Bonn Econ Discussion Papers bgse17_2001, University of Bonn, Germany.
    2. Serafín Frache & Gabriel Katz, 2004. "Estimating a Risky Term Structure of Uruguayan Sovereign Bonds," Documentos de Trabajo (working papers) 0304, Department of Economics - dECON.

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