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Abstract and Applied Analysis
Volume 2014, Article ID 580713, 17 pages
Research Article

The Dynamic Spread of the Forward CDS with General Random Loss

1Department of Mathematics, Shanghai Jiao Tong University, Shanghai 200240, China
2School of Business Information, Shanghai University of International Business and Economics, Shanghai 201620, China

Received 24 February 2014; Accepted 3 May 2014; Published 27 May 2014

Academic Editor: Igor Leite Freire

Copyright © 2014 Kun Tian et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


We assume that the filtration is generated by a -dimensional Brownian motion as well as an integer-valued random measure . The random variable is the default time and is the default loss. Let be the progressive enlargement of by ; that is, is the smallest filtration including such that is a -stopping time and is -measurable. We mainly consider the forward CDS with loss in the framework of stochastic interest rates whose term structures are modeled by the Heath-Jarrow-Morton approach with jumps under the general conditional density hypothesis. We describe the dynamics of the defaultable bond in and the forward CDS with random loss explicitly by the BSDEs method.