In this work we propose an approximate numerical method for pricing of options for the constant elasticity of variance (CEV) diffusion model. We prove firstly the existence and uniqueness of the solution in weighted Sobolev space, and then we propose the finite element method and finite difference method to solve the considered problem. Therefore, we compare the obtained results by the two approaches, with those given by the Monte Carlo method in Broadie-Kaya [6], using two simulation techniques : the exact method and the Euler discretization. A comparative numerical study is done using some values of the coefficient of elasticity