Essays on Diversification of Financial Portfolios and Structured Credit Funds: A Copula Approach.

Summary In this thesis, we examine the important contributions of dependence modeling by copula theory in the context of problems related to the management of financial portfolios and structured credit products.The first part of this thesis is devoted to the management of financial portfolios. The first part of this thesis is devoted to the management of financial portfolios. We first study the relationship that can be established between the level of diversification of the portfolio and the choice of the copula that best describes the dependency structure. The objective is to identify a characteristic in the portfolios allowing a simpler selection of the appropriate copula. In a second chapter, we propose to study the impact of a misspecification of the copula model on the estimates of conventional risk measures such as Value-at-Risk and Expected-Shortfall. The idea is to verify the usefulness of developing these estimates under the true copula model. In a third chapter, we study the impact of a misspecification of the copula model in the context of an optimal portfolio allocation problem. The main objective is to identify the sensitivity of investors, according to their degree of risk aversion (losses), for one or the other component of the copula model. We propose to establish a bridge between the teachings of behavioral finance theories and the modeling of dependence by the copula theory.The second part of the thesis deals with structured credit products. We study, in a first chapter, the contribution of an actuarial model, using copula functions in the modeling of the dependence structure between default times, in the context of the estimation process of risk measures. Finally, in a last chapter we revisit the notion of the "Diversity Score", developed by the rating agency Moody's in order to assign the quality of structured credit products in terms of diversification. We discuss the analogy of this measure with that of the copula approach, and we demonstrate its adequacy with some families of copula functions.