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# Modeling the forward CDS spreads with jumps

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XIONG, Dewen, Michael KOHLMANN, 2012. Modeling the forward CDS spreads with jumps. In: Stochastic Analysis and Applications. 30(3), pp. 375-402. ISSN 0736-2994. Available under: doi: 10.1080/07362994.2012.668435

@article{Xiong2012Model-19120, title={Modeling the forward CDS spreads with jumps}, year={2012}, doi={10.1080/07362994.2012.668435}, number={3}, volume={30}, issn={0736-2994}, journal={Stochastic Analysis and Applications}, pages={375--402}, author={Xiong, Dewen and Kohlmann, Michael} }

Modeling the forward CDS spreads with jumps Kohlmann, Michael 2012-04-24T07:08:38Z Publ. in: Stochastic Analysis and Applications ; 30 (2012), 3. - pp. 375-402 terms-of-use 2012-04-24T07:08:38Z We consider the forward CDS in the framework of stochastic interest rates whose term structures are modeled in the sense of the Heath-Jarrow-Morton model with jumps adapted to a filtration $\bb F$(see \cite{Xiong-Kohlmann2010b}). Under the assumption that the density process of the default is a bounded $\bb F$-predictable process, we obtain a quadratic-exponential type system of BSDEs similar to \cite{Xiong-Kohlmann2010b} which always has a unique solution $(X,\theta,\vartheta)$. By the solution of such a system of BSDEs, we will describe the dynamics of the the pre-default values of the defaultable bond, the defaultable forward Libor rates and the restricted defaultable forward measure (see in \cite{Eberlein-Kluge-Schoenbucher-2006}) explicitly. Then we introduce another quadratic-exponential type system of BSDEs (called \textbf{adjoint system of BSDEs}) which also always has a unique solution, and using this solution, we describe the dynamic of the fair spread of the forward CDS with the tenor structure $\bb T =\{a=T_0 < T_1 < \cdots< T_n=b\}$ explicitly. Xiong, Dewen eng 2012 Xiong, Dewen Kohlmann, Michael