Density Approach in Modeling Successive Defaults

We apply the density framework developed in [N. El Karoui, M. Jeanblanc, and Y. Jiao, Stochastic Process. Appl., 120 (2010), pp. 1011–1032] to the modeling of successive multiple defaults. Under the hypothesis of existence of the joint density of the ordered default times with respect to a reference filtration, we present general pricing results and establish links with the classical intensity approach; in particular, we emphasize the impact of default events at successive default times. Explicit models, constructed using the methods of change of probability measure or dynamic copula, are proposed.