Monte-Carlo methods and low-discrepancy sequences applied to the calculation of options in finance.

Summary This thesis contains two parts: the first part deals with numerical methods and the second part studies their applications in finance. The first chapters are devoted to a description of Monte-Carlo, quasi Monte-Carlo and hybrid methods. We give an estimate of the variation of a function and techniques to reduce it. We also give an estimate of the extended discrepancy of one-dimensional sequences, in particular those whose terms are a sum of components of a multidimensional sequence with low discrepancy. Then, the last chapters focus on the valuation and hedging of options with one or more risky assets, such as a European call in a full market model with jumps, an Asian call in an incomplete market model with jumps or a basket call in a multidimensional Black-Scholes model. We obtain many numerical results and prove that some functions from finance are not finite variable.