TAILIEUCHUNG - Reduced form modelling for credit risk

The purpose of this paper is to present in a uni¯ed 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-¯ltrations, 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 ¯ltration is considered reveals to be non tractable in most of cases, whereas. | Reduced form modelling for credit risk Monique Jeanblancf Yann Le Camg V Université d Evry Val d Essonne 91025 Evry Cedex France t Institut Europlace de Finance Í French Treasury November 12 2007 Abstract 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. Introduction Given the flow of information of a financial market containing both defaultable and default free assets the methodology for modelling a credit event can be split into two main approaches The structural approach chronologically the first one and the reduced form approach. In the structural framework the credit event is modelled as the hitting time of a barrier by a process adapted to the information flow typically the value of the firm crossing down a debt ratio . This approach is intuitive refereing to economic fundamentals such as for example the structure of the balance sheet of the company and the valuation and hedging theory relies on tools close to the techniques involved in the classical Black and Scholes default-free set up. Nonetheless it presents important drawbacks the value process can not be easily observed it is not a tradeable security a relevant trigger is very complex to identify. Moreover a simple continuous firm s value process implies a predictable credit event leading to .

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