Hazard rate for credit risk and hedging defaultable contingent claims
The authors study an arbitrage free financial market, where a risk-free asset \(S^0\) and a risky asset \(S\) are traded. The model is presented, including filtration, equivalent martingale measure, hazard process, martingale decomposition and general representation theorem. Then, the role of the hypothesis of the invariance of martingales is discussed and it is established that this hypothesis holds as soon as the default-free market is complete and arbitrage free, and the defaultable market is arbitrage free. It is proved that under some regularity condition, the default time is the first time when a stochastic barrier is reached as in Cox process modeling. The main result that to hedge a defaultable claim, one has to invest the value of this contingent claim in the Defaultable Zero-Coupon (DZC). This results are linked with the hazard process approach: the default arrives so that the jump in the hedging portfolio value is equal to the jump in the DZC.
scientific article; zbMATH DE number 2118693