This project will focus on the numerical estimation of financial options. The latter are contracts associated to financial objects such as stocks, which can be mathematically expressed as expectations with respect to a diffusion process. In this project, we will develop Monte Carlo methods which can provide numerical estimates of these option prices, which are not available in closed forms. In particular, the diffusion processes will have to be time-discretized and we will use advanced multilevel and unbiased techniques to provide estimates sometimes with no time-discretization error.​