Reduced form modelling for credit risk

The purpose of this paper is to present in a unified context the reduced form modelling approach, in which a credit event is modelled as a totally inaccessible stopping time. Once the general framework is introduced (frequently referred to as “pure intensity” set-up), we focus on the special case where the full information at the disposal of the traders may be split in two sub-filtrations, one of them carrying the full information of the occurrence of the credit event (in general referred to as “hazard process” approach). The general pricing rule when only one filtration is considered reveals to be non tractable in most of cases, whereas the second construction leads to much simplest formulas. Examples are given and evidence advanced that this set-up is more tractable.