Hazard rate for credit risk and hedging defaultable contingent claims

We provide a concise exposition of theoretical results that appear in modeling default time as a random time, we study in details the invariance martingale property and we establish a representation theorem which leads, in a complete market setting, to the hedging portfolio of a vulnerable claim. Our main result is that, to hedge a defaultable claim one has to invest the value of this contingent claim in the defaultable zero-coupon.Received: April 2003Mathematics Subject Classification: 91B24, 91B29, 60G46JEL Classification: G10The authors would like to thank D. Becherer and J.N. Hugonnier for interesting discussions and the anonymous referee whose pertinent questions on the first version of this paper help them to clarify the proofs. All remaining errors are ours.