Statistical modeling in finance and estimation of diffusion processes.

Summary The first part of this paper presents asset pricing models based on the principle of no arbitrage opportunities and compatible with statistical analysis. Such models are described in discrete time. We first focus on the study of the term structure of interest rates and on the estimation of such a model from the observation of fixed income bonds. We then extend the proposed approach to more complex securities. We then describe a valuation model where statistical randomness appears in the price dynamics of elementary contingent assets. The properties of this model are studied when the price law of the elementary contingent assets is a gamma measure and we show in particular that it allows to generalize classical valuation formulas. The second part of this thesis is devoted to estimation problems in diffusion processes. First, we present the different parametric or nonparametric estimation methods by classifying them by asymptotics. Then we study the properties of parametric estimators of a diffusion from discrete time observations, with a fixed step. The estimation methods used are methods based on simulations of the process: simulated moments and indirect inference. We focus on establishing explicit links between the different asymptotics that appear and the number of observations.