This paper, inspired by recent advances in the application of the multilevel Monte-Carlo (MLMC) approach to Lévy driven assets, is based on the valuation of financial derivatives. First, using the weak Euler method the numerical estimate of the underlying asset, which satisfies a multi-dimensional stochastic differential equation with Lévy noise, is calculated and then applying the weak multilevel Monte-Carlo method the expected price is obtained. In this paper, as an improvement of Belomestny’s work and with a new approach in the theory, we express and prove the convergence theorems in spacefor and not only 2. We also seek to implement the weak MLMC algorithm for nonlinear equations with dependent components and . In the end, we show numerical experiments when applied to different types of processes with call options../files/site1/files/72/14Abstract.pdf