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Martedi' 29 Aprile 2008 alle ore 16:00 in aula 1A/150 della Torre Archimede la Professoressa Monique Jeanblanc (Univ. d'Evry) terra' una conferenza della serie Colloquia Patavina dal titolo "Some problems in credit risk modelling". Trovate qui sotto un sommario della conferenza ed un link alla pagina web del relatore.
La Commissione Colloquia
M. A. Garuti, M. Pavon, M. Pitteri, F. Rossi
Some problems in credit risk modelling
Monique Jeanblanc (Univ. d'Evry)
Pagina web: http://www.maths.univ-evry.fr/pages_perso/jeanblanc/
Martedi' 29 Aprile 2008, ore 16:00
Aula: 1A/150, Torre Archimede
In this talk, I shall present some mathematical problems that appear while studying credit risk. This presentation is based on works with various co-authors (Bielecki, T., Le Cam, Y., Rutkowski, M.).
There are two main models for credit risk modelling: the structural approach and the reduced form approach. In the structural approach, the default time is the first hitting time of a deterministic level by an observable continuous process, hence is a predictable stopping time. The reduced form approach corresponds to a totally inaccessible stopping time. Using a partial observation approach, it is easy to
restrict the information and to transform a structural approach to a reduced form approach. One can also assume that the process which triggers the default is not observable and that the observation is a correlated process. It is well known that structural models produce spreads that are far from the observed ones, this is no longer the
case in the restricted information setting.
A standard framework is to start from the knowledge of the conditional law of the default, with respect to a reference filtration F, and to enlarge this filtration with the observation of the default time. However, default times are not honest, i.e., one can not apply the usual theory of enlargement of filtration. Under some hypotheses, martingales in the reference filtration remain semi-martingales in the enlarged filtration, and one can provide the semi-martingale decomposition of the F-martingales. A predictable representation theorem can be established. The role of immersion property (when F-martingales remain martingales in the enlarged filtration) is studied in this financial context.
The role of the reference filtration and of immersion hypothesis is important while studying the multi-name setting. In that case, immersion hypothesis does not hold and the semi-martingale decomposition is essential to obtain the dynamics of defaultable assets (as Credit Default Swaps) in the filtration which contains information of the defaults which occurred in the past. We present some examples.