  We consider the so-called $\natural$-model. It is an one-default model which
gives the conditional law of a random time with respect to a reference
filtration. This model has been studied in the case where the parameters are
continuous. In this paper we will establish the $\natural$-model in the case of
jump parameters. We then prove the corresponding enlargement of filtration
formula and we compute the derivative of the conditional distribution functions
of the random time.
