  The intensity of a default time is obtained by assuming that the default
indicator process has an absolutely continuous compensator. Here we drop the
assumption of absolute continuity with respect to the Lebesgue measure and only
assume that the compensator is absolutely continuous with respect to a general
$\sigma$-finite measure. This allows for example to incorporate the
Merton-model in the generalized intensity based framework. An extension of the
Black-Cox model is also considered. We propose a class of generalized Merton
models and study absence of arbitrage by a suitable modification of the forward
rate approach of Heath-Jarrow-Morton (1992). Finally, we study affine term
structure models which fit in this class. They exhibit stochastic
discontinuities in contrast to the affine models previously studied in the
literature.
