Hazard Processes and Martingale Hazard Processes

In this paper, we build a bridge between different reduced-form approaches to pricing defaultable claims. In particular, we showhow the well known formulas by Duffie et al. [12] and by Elliott et al.[14] are related. Moreover, in the spirit of Collin Dufresne et al. [8], wepropose a simple pricing formula under an equivalent change of measure.Two processes will play a central role: the hazard process and themartingale hazard process attached to a default time. The crucial stepis to understand the difference between them, which has been an openquestion in the literature so far.[...]