Default Risk: An Enlargement of Filtration Approach

Abstract

In this chapter, our goal is to present results that cover the reduced form methodology of credit risk modelling. In the first part, we provide a detailed analysis of the relatively simple case where the flow of information available to an agent reduces to observations of the random time which models the default event. The focus is on the evaluation of conditional expectations with respect to the filtration generated by a default time by means of the hazard function. In the second part, we study the case where an additional information flow is present; we then use the conditional survival probability, also called the hazard process. We present the intensity approach and discuss the link between both approaches. After a short introduction to Credit Default Swap’s, we end the chapter with a study of hedging defaultable claims.