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Multiname default modeling is crucial in the context of pricing credit derivatives such as Collaterized Debt Obligations (CDOs). We consider here a simple reduced form approach for multiname defaults based on the Vasicek or Ornstein-Uhlenbeck model for the hazard rates of the underlying names. We analyze the impact of volatility time scales on the default distribution and CDO prices. We demonstrate how correlated ∞uctuations in the parameters of the name hazard rates afiect the loss distribution and senior tranches of CDOs. The efiect of stochastic parameter ∞uctuations is to change the shape of the loss distribution and cannot be captured by using averaged parameters in the original model. Our analysis assumes a separation of time scales and leads to a singular-regular perturbation problem (7, 8). This framework allows us to compute perturbation approximations that can be used for efiective pricing of CDOs.

Multiname and Multiscale Default Modeling