Asset value is a stochastic process whose dynamics is modeled by a stochastic differential equation. Given the specific features of an asset, this equation can be continuous or with jumps. Considering the possibility of lacking an analytical solution or the difficulty of calculating it, we need to be able to estimate the solution numerically in order to know the financial derivative price at any given moment. A financial derivative is a tool based on the value of an underlying asset, such as bonds, and it is effective for reducing the risk of investment. To price a financial derivative we need to compute an expected value. In this thesis, we consider the multilevel Monte-Carlo method for calculating the expected value of an underlying asset as $ \\E [f (X_t)] $, where $ f $ is the payoff function of the financial derivative. For this purpose, we study the numerical solution of the stochastic differential equation in diffusion and jump-diffusion models and estimate the expected value using the weak multilevel Monte-Carlo method.