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# Defaultable Bond Markets with Jumps

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XIONG, Dewen, Michael KOHLMANN, 2012. Defaultable Bond Markets with Jumps. In: Stochastic Analysis and Applications. 30(2), pp. 285-321. ISSN 0736-2994. Available under: doi: 10.1080/07362994.2012.649623

@article{Xiong2012Defau-18544, title={Defaultable Bond Markets with Jumps}, year={2012}, doi={10.1080/07362994.2012.649623}, number={2}, volume={30}, issn={0736-2994}, journal={Stochastic Analysis and Applications}, pages={285--321}, author={Xiong, Dewen and Kohlmann, Michael} }

eng Stochastic Analysis and Applications ; 30 (2012), 2. - S. 285-321 deposit-license We construct a model for the term structure in a market of defaultable bonds with jumps $\{p^d(t,T);t\le T\}$, $T\in(0,T^*]$. We derive the instantaneous defaultable forward rate $f^d(t,T)$ defined by $p^d(t,T)=\bb I_{\{t<\tilde\tau\}}e^{-\int_t^Tf^d(t,l)dl}$ in the real world probability. We are also given default-free bonds $\{p(t,T);t\le T\}$, $T\in(0,T^*]$ and we establish the market consisting of both the defaultable and the non-defaultable bonds. In this market we study the common equivalent martingale measure and in this arbitrage free market we derive the relationship between the forward rates $f(t,T)$ and $f^d(t,T)$ associated with the two sorts of bonds. Especially, it is proved that in a parameterized market with common equivalent martingale measure where $f(t,T)$ can be described by (\ref{eqn-forward rate-1}) the defaultable forward rate $f^d(t,T)$ can be reconstructed from the special form of the default-free forward rate $f(t,T)$ if a certain system of BSDEs has a solution.\\ Finally we extend the results to a market with recovery rate and give examples where the system of BSDEs has a solution.\\ 2012-02-20T15:59:37Z 2012-02-20T15:59:37Z Xiong, Dewen Xiong, Dewen Defaultable Bond Markets with Jumps Kohlmann, Michael 2012 Kohlmann, Michael