Study of correlation and incompleteness problems in credit markets.

Summary We study issues related to the valuation and hedging of basket credit derivatives. In particular, we are interested, on the one hand, in the modeling of default correlation and, on the other hand, in the market incompleteness introduced by the correlation risk. This thesis also contributes to the literature on numerical methods for valuing basket products. In the first chapter, we study the conditional-hop diffusion approach and the impact of filter magnification on the dynamics of intensity processes. The second chapter is devoted to the Marshall-Olkin copula. A detailed study of its properties is made, as well as the parameterization of this correlation structure. In the third chapter, we develop semi-analytical methods to evaluate basket credit derivatives in a Marshall-Olkin model. In the fourth chapter, we solve the hedging problem of basket products. Finally, in the fifth chapter, we analyze the correlation risk found in a new generation of products known as CDO-squared.