Risk Analysis and Hedging of Synthetic CDO Tranches.

Summary The purpose of this thesis is to shed light on some aspects of risk management of synthetic CDO tranches. The first part deals with the risk analysis of CDO tranches in the class of factor models which includes a large number of popular approaches such as copula-based models, multivariate structural models, multivariate Poisson models or affine intensity models. Moreover, when considering a homogeneous credit portfolio, the assumption of a dependence structure based on a factor representation is no longer restrictive thanks to De Finetti's theorem. The law of conditional probability of default plays an important role in the evaluation of CDO tranches but also in the risk analysis of credit portfolios. Indeed, it is possible to compare different factor models by simply comparing their conditional probability of default. The second part addresses the hedging problem in the context of Markov contagion models for which the prices of assets contingent on default risk can be perfectly replicated under the assumption of no simultaneous defaults. Moreover, when the portfolio is homogeneous and when default intensities depend only on the current state of the number of defaults, the aggregate loss process is simply a Markov chain. In this case, it is possible to calibrate the aggregate loss intensities on a loss distribution and to efficiently compute dynamic hedging strategies using a recombining binomial tree in which the payoff of the CDO tranches can be perfectly duplicated thanks to the index and the risk-free asset.