Ying Jiao
U.F.R. de Mathématiques
Université Paris 7

Density approach in the credit risk modelling

To analyze the impact of a default event, we propose a new credit risk 
modelling framework which is based on the conditional density of default 
with respect to the "default-free" filtration and on the progressive 
enlargement of filtration. We first distinguish different types of 
information and clarify the link with the widely-used credit intensity 
approach. We then establish a martingale characterization result in the 
enlarged filtration which allows to propose "after-default" density models 
by using a Girsanov's theorem. Further applications show that this approach 
is efficient in dealing with counterparty risks and with multiple defaults.