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Default compensator, incomplete information, and the term structure of credit spreads

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  • Giesecke, Kay
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    Abstract

    We provide a framework for the analysis of term structures of credit spreads on corporate bonds in the presence of informational asymmetries. While bond investors observe default incidents, we suppose that they have incomplete information on the firm's assets and/or the threshold asset level at which informed equity investors liquidate the firm. As a natural tool for the characterization of conditional default probabilities, prices of default-contingent claims, and credit spreads, we construct the compensator of default in terms of investors' threshold prior and the conditional running minimum asset distribution. With perfect asset observation, a new phenomenon appears: the default compensator is singular. Here an arrival intensity for default does not exist even though the default is completely unpredictable. In a setting where the assets of the firm follow a geometric Brownian motion, we show that the term structure of credit spreads is decreasing or hump-shaped, depending on the level of the current asset value. Spreads for maturities going to zero are only positive if the assets are at an historic low and the firm is quite risky. With imperfect asset observation, an arrival intensity for default does exist. This intensity is characterized through the compensator. In the geometric Brownian motion setting, the spread term structure is always decreasing with strictly positive spreads. --

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    Bibliographic Info

    Paper provided by Humboldt University of Berlin, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes in its series SFB 373 Discussion Papers with number 2002,8.

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    Date of creation: 2001
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    Handle: RePEc:zbw:sfb373:20028

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    Keywords: incomplete information; compensator; credit spreads; intensity;

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    1. 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 351-67, May.
    2. 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.
    3. Harrison, J. Michael & Kreps, David M., 1979. "Martingales and arbitrage in multiperiod securities markets," Journal of Economic Theory, Elsevier, vol. 20(3), pages 381-408, June.
    4. Anderson, Ronald W & Sundaresan, Suresh, 1996. "Design and Valuation of Debt Contracts," Review of Financial Studies, Society for Financial Studies, vol. 9(1), pages 37-68.
    5. Duffie, Darrell & Lando, David, 2001. "Term Structures of Credit Spreads with Incomplete Accounting Information," Econometrica, Econometric Society, vol. 69(3), pages 633-64, May.
    6. 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.
    7. Sarig, Oded & Warga, Arthur, 1989. " Some Empirical Estimates of the Risk Structure of Interest Rates," Journal of Finance, American Finance Association, vol. 44(5), pages 1351-60, December.
    8. Merton, Robert C., 1973. "On the pricing of corporate debt: the risk structure of interest rates," Working papers 684-73., Massachusetts Institute of Technology (MIT), Sloan School of Management.
    9. Philippe Artzner & Freddy Delbaen, 1995. "Default Risk Insurance And Incomplete Markets," Mathematical Finance, Wiley Blackwell, vol. 5(3), pages 187-195.
    10. Hayne E. Leland., 1994. "Corporate Debt Value, Bond Covenants, and Optimal Capital Structure," Research Program in Finance Working Papers RPF-233, University of California at Berkeley.
    11. Duffie, Darrell & Singleton, Kenneth J, 1999. "Modeling Term Structures of Defaultable Bonds," Review of Financial Studies, Society for Financial Studies, vol. 12(4), pages 687-720.
    12. Geske, Robert, 1979. "The valuation of compound options," Journal of Financial Economics, Elsevier, vol. 7(1), pages 63-81, March.
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    Cited by:
    1. Giesecke, Kay, 2001. "Correlated default with incomplete information," SFB 373 Discussion Papers 2002,30, Humboldt University of Berlin, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes.

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