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A lattice model with incomplete information: A credit risk application

Author

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  • Cherubini Umberto
  • Mulinacci Sabrina

    (University of Bologna, Dept. of Mathematical Economics, Bologna, Italien)

  • Romagnoli Silvia

    (University of Bologna, Dept. of Mathematical Economics, Bologna, Italien)

Abstract

We design a discrete time arbitrage-free model under incomplete information for application to credit risk models in the spirit of Duffie and Lando (2001). We assume a fundamental value process evolving according to a complete market model and a sequence of imperfect signals conveying information on the state of the fundamental value. The market value is computed by conditioning on the available information. The model shows that if the information setting is built consistently, the market remains complete even in the face of incomplete information. If insiders are not allowed into the market, the requirement is that the equivalent martingale measure of market prices has to coincide with the martingale measure of the fundamental price in the case of perfect information (Information Consistency). Such martingale measure can be recovered for arbitrary dependence structures between the fundamental process and the signal. If insiders are allowed into the market, the Information Consistency requirement has to be made more stringent by imposing the H-condition. We show that in this case only a subset of signals are consistent with no arbitrage, and are those that are not-Granger caused by the fundamental process. The model is finally applied to the study of the dynamics of the expected loss of a BBB rated firm in presence of incomplete information.

Suggested Citation

  • Cherubini Umberto & Mulinacci Sabrina & Romagnoli Silvia, 2008. "A lattice model with incomplete information: A credit risk application," Statistics & Risk Modeling, De Gruyter, vol. 26(2), pages 75-88, March.
    • Handle: RePEc:bpj:strimo:v:26:y:2008:i:2:p:75-88:n:2
    DOI: 10.1524/stnd.2008.0914
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    References listed on IDEAS

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    1. Delia Coculescu & Hélyette Geman & Monique Jeanblanc, 2008. "Valuation of default-sensitive claims under imperfect information," Finance and Stochastics, Springer, vol. 12(2), pages 195-218, April.
    2. Yu, Fan, 2005. "Accounting transparency and the term structure of credit spreads," Journal of Financial Economics, Elsevier, vol. 75(1), pages 53-84, January.
    3. 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.
    4. 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 449-470, May.
    5. Leland, Hayne E, 1994. "Corporate Debt Value, Bond Covenants, and Optimal Capital Structure," Journal of Finance, American Finance Association, vol. 49(4), pages 1213-1252, September.
    6. 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 637-654, May-June.
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