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On a variational formulation used in credit risk modeling

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  • Pacelli, Graziella
  • Ballestra, Luca Vincenzo

Abstract

We consider the credit risk model of Collin-Dufresne and Goldstein (2001). According to this model, the price of a defaultable bond can be efficiently computed using a variational formulation that consists of an integral relation and a Volterra integral equation. In Collin-Dufresne and Goldstein (2001) this integral equation is justified by a probabilistic intuition, but is not proven formally. In this paper we analytically derive the variational formulation used in Collin-Dufresne and Goldstein (2001). This analysis allows to give a correct characterization of the solution of the integral equation. Furthermore the approach proposed in this paper could also be employed for other models of credit risk.

Suggested Citation

  • Pacelli, Graziella & Ballestra, Luca Vincenzo, 2010. "On a variational formulation used in credit risk modeling," Finance Research Letters, Elsevier, vol. 7(2), pages 110-118, June.
    • Handle: RePEc:eee:finlet:v:7:y:2010:i:2:p:110-118
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    References listed on IDEAS

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    1. Vasicek, Oldrich, 1977. "An equilibrium characterization of the term structure," Journal of Financial Economics, Elsevier, vol. 5(2), pages 177-188, November.
    2. Vasicek, Oldrich Alfonso, 1977. "Abstract: An Equilibrium Characterization of the Term Structure," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 12(4), pages 627-627, November.
    3. Pierre Collin‐Dufresne & Robert S. Goldstein, 2001. "Do Credit Spreads Reflect Stationary Leverage Ratios?," Journal of Finance, American Finance Association, vol. 56(5), pages 1929-1957, October.
    4. Longstaff, Francis A & Schwartz, Eduardo S, 1995. "A Simple Approach to Valuing Risky Fixed and Floating Rate Debt," Journal of Finance, American Finance Association, vol. 50(3), pages 789-819, July.
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