Density models and applications to counterparty credit risk.

Summary This thesis deals with density models for default times and their application to credit and counterparty risk. The first part is a theoretical contribution to the study of projections on different filtrations of the Radon-Nikodym density, in the form of Doleans-Dade exponential, occurring during measurement changes. The main result is the characterization of the measurement changes that preserve the immersion, obtained by applying our projection formulas. The second part aims at an informational dynamization of the static Gaussian copula model applied to a credit portfolio, which can be seen as a density model allowing to deal with CDO hedging by CDS or counterparty risk on credit derivatives. The main contributions are the introduction of the dynamic perspective, which gives a theoretical justification to the Gaussian copula bump-sensitivities used by practitioners, and the application to CVA calculations on a CDS.