Abstracts

Credit risk is typically either treated with a structural viewpoint pioneered in Merton (1974) or the reduced-form framework as in Jarrow \& Turnbull (1995). The goal of this article is to provide a unified view on both approaches in a sufficiently generalized setup. The considered model allows for default times which have an intensity \emph{or} occur at a fixed time with positive probability, henceforth not avoiding stopping times. A forteriori, the considered default times do not fall in the class of so-called intensity-based models.
The setup is intimately related to the theory of enlargement of filtrations, to which we provide a new class of examples where the Az\`ema supermartingale contains jumps, both at predictable and totally inaccessible stopping times. In the second part of the paper dynamic term structures prone to default risk in the framework of Heath-Jarrow-Morton (1992). It turns out, that previously considered models in this framework lead to arbitrage possibilities. We propose a suitable, arbitrage-free generalization of this class with an additional stochastic integral containing atoms at predictable stopping time.