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.

" On a variational formulation used in credit risk modeling".

PACELLI, GRAZIELLA
2010-01-01

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.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11566/32276
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