On filtration immersions and credit events∗

In credit risk models, it is usually assumed that the intensity processes contain all the necessary information about the default times. This is indeed the case when the appropriate immersion properties hold, so that one can compute the conditional law of the default times in terms of the intensity processes. In this paper, we characterize the immersion properties in terms of the terminal values of the compensators of the default processes. We also give an example of a model in which the immersion property does not hold, and the conditional law of the default times depend on the intensity and some other process.