Quantification and statistical methods for model risk.

Summary In finance, model risk is the risk of financial loss resulting from the use of models. It is a complex risk to apprehend and covers several very different situations, especially the estimation risk (a model generally uses an estimated parameter) and the model specification error risk (which consists in using an inadequate model). This thesis focuses on the quantification of model risk in the construction of rate or credit curves and on the study of the compatibility of Sobol indices with the theory of stochastic orders. It is divided into three chapters. Chapter 1 deals with the study of model risk in the construction of rate or credit curves. In particular, we analyze the uncertainty associated with the construction of rate or credit curves. In this context, we have obtained no-arbitrage bounds associated with implied default or rate curves that are perfectly compatible with the quotations of the associated reference products. In Chapter 2 of the thesis, we make the link between global sensitivity analysis and stochastic order theory. In particular, we analyze how the Sobol indexes transform following an increase in the uncertainty of a parameter in the sense of the stochastic dispersive order or excess wealth. Chapter 3 of the thesis focuses on the quantile contrast index. We first make the link between this index and the CTE risk measure, and then we analyze the extent to which an increase in the uncertainty of a parameter in the sense of stochastic dispersive order or excess wealth leads to an increase in the quantile contrast index. Finally, we propose a method for estimating this index. We show, under appropriate assumptions, that the estimator we propose is consistent and asymptotically normal.