What happens after a default: the conditional density approach

Nicole El Karoui (1, 2) , Monique Jeanblanc (3) , Ying Jiao (1)

1 LPMA - Laboratoire de Probabilités et Modèles Aléatoires
2 CMAP - Centre de Mathématiques Appliquées - Ecole Polytechnique
3 Département de Mathématiques (Evry)

We present a general model for default time, making precise the role of the intensity process, and showing that this process allows for a knowledge of the conditional distribution of the default only ``before the default". This lack of information is crucial while working in a multi-default setting. In a single default case, the knowledge of the intensity process does not allow to compute the price of defaultable claims, except in the case where immersion property is satisfied. We propose in this paper the density approach for default time. The density process will give a full characterization of the links between the default time and the reference filtration, in particular ``after the default time". We also investigate the description of martingales in the full filtration in terms of martingales in the reference filtration, and the impact of Girsanov transformation on the density and intensity processes, and also on the immersion property.

Domaines: Probabilités [math.PR]

Nicole El Karoui, Monique Jeanblanc, Ying Jiao. What happens after a default: the conditional density approach. 2009. ⟨hal-00381090⟩