Interest rate and exchange rate options valuation.

Summary This thesis has five chapters. In the first chapter, we return to the theory of expectations. After a reminder of the basic notions, we give two new formulations of the expectations hypotheses. The first one is obtained in the framework of the quadratic Gaussian model. The second one is obtained in the case of a diffusion model with jumps. In the second chapter, two problems are exposed: the long rate problem and the problem of affine factorial models in the presence of jumps. First, we show that the long rate is a random process. Then, we obtain new constraints on the rate curve in the framework of affine factorial models. The third chapter is inspired by a work done by el karoui and cherif (1992) on multi-currency arbitrage. After a reminder of some known results, we give the new arbitrage relations in the framework of a discontinuous model. Then, we study some quanto options. The first part of the fourth chapter is a complement to the third. In the second part, we study some quanto-barrier options and level barriers. In the last part, examples on the terminal wealth maximization problem are presented in detail. The last chapter studies the exchange rate: the problems of intervention in a target zone regime and the problem of the single currency are discussed.