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We model the term structure of the forward default intensity and the defaultdensity by using L\'evy random fields, which allow us to consider the creditderivatives with an after-default recovery payment. As applications, we studythe pricing of a defaultable bond and represent the pricing kernel as theunique solution of a parabolic integro-differential equation. Finally, weillustrate by numerical examples the impact of the contagious jump risks on thedefaultable bond price in our model.

Credit derivatives pricing with default density term structure modelled by L\'evy random fields