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. © 2010 Elsevier Inc. All rights reserved.
On a variational formulation used in credit risk modeling / Pacelli, Graziella; Ballestra, Luca Vincenzo. - In: FINANCE RESEARCH LETTERS. - ISSN 1544-6123. - STAMPA. - 7:2(2010), pp. 110-118. [10.1016/j.frl.2010.01.002]
On a variational formulation used in credit risk modeling
BALLESTRA, LUCA VINCENZO
2010
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. © 2010 Elsevier Inc. All rights reserved.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
