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A General Framework for Incorporating Stochastic Recovery in Structural Models of Credit Risk

Author

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  • Albert Cohen

    (Department of Mathematics, Michigan State University, East Lansing, MI 48824, USA)

  • Nick Costanzino

    (Quantitative Analytics, Barclays Capital, 745 7th Ave, New York, NY 10019, USA)

Abstract

In this work, we introduce a general framework for incorporating stochastic recovery into structural models. The framework extends the approach to recovery modeling developed in Cohen and Costanzino (2015, 2017) and provides for a systematic way to include different recovery processes into a structural credit model. The key observation is a connection between the partial information gap between firm manager and the market that is captured via a distortion of the probability of default. This last feature is computed by what is essentially a Girsanov transformation and reflects untangling of the recovery process from the default probability. Our framework can be thought of as an extension of Ishizaka and Takaoka (2003) and, in the same spirit of their work, we provide several examples of the framework including bounded recovery and a jump-to-zero model. One of the nice features of our framework is that, given prices from any one-factor structural model, we provide a systematic way to compute corresponding prices with stochastic recovery. The framework also provides a way to analyze correlation between Probability of Default (PD) and Loss Given Default (LGD), and term structure of recovery rates.

Suggested Citation

  • Albert Cohen & Nick Costanzino, 2017. "A General Framework for Incorporating Stochastic Recovery in Structural Models of Credit Risk," Risks, MDPI, vol. 5(4), pages 1-19, December.
    • Handle: RePEc:gam:jrisks:v:5:y:2017:i:4:p:65-:d:123567
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    References listed on IDEAS

    as
    1. 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.
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    3. Merton, Robert C., 1976. "Option pricing when underlying stock returns are discontinuous," Journal of Financial Economics, Elsevier, vol. 3(1-2), pages 125-144.
    4. Albert Cohen & Nick Costanzino, 2017. "Bond and CDS Pricing via the Stochastic Recovery Black-Cox Model," Risks, MDPI, vol. 5(2), pages 1-28, April.
    5. Chunsheng Zhou, 1997. "A jump-diffusion approach to modeling credit risk and valuing defaultable securities," Finance and Economics Discussion Series 1997-15, Board of Governors of the Federal Reserve System (U.S.).
    6. Das, Sanjiv R. & Hanouna, Paul, 2009. "Implied recovery," Journal of Economic Dynamics and Control, Elsevier, vol. 33(11), pages 1837-1857, November.
    7. Wang, Shaun S., 2002. "A Universal Framework for Pricing Financial and Insurance Risks," ASTIN Bulletin, Cambridge University Press, vol. 32(2), pages 213-234, November.
    8. Peter Carr, 2017. "Bounded Brownian Motion," Risks, MDPI, vol. 5(4), pages 1-11, November.
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    Cited by:

    1. Castellano, Rosella & Corallo, Vincenzo & Morelli, Giacomo, 2022. "Structural estimation of counterparty credit risk under recovery risk," Journal of Banking & Finance, Elsevier, vol. 140(C).

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