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.
Kun Tian. Dewen Xiong. Zhongxing Ye. "The Dynamic Spread of the Forward CDS with General Random Loss." Abstr. Appl. Anal. 2014 (SI37) 1 - 17, 2014. https://doi.org/10.1155/2014/580713