In this work, we numerically solve a multi-asset European call option with the finite difference method (FDM) and take the advantages of the antithetic Monte Carlo simulation as a variance reduction technique in the end point of the domain, and the linear boundary condition has been implemented in other boundaries. We also apply the grid stretching transformation to make a non-equidistance discretization with more nodal points around the strike price which is the non-smooth point in the payoff function to reduce the numerical errors around this point and have more accurate results. Superiority of our method (GSMCBC) will be demonstrated by comparison with the standard finite difference scheme with the equidistance discretization and the linear boundary conditions (LBC) and also combination of the LBC scheme with the standard Monte Carlo simulation at the end point of the domain (MCBC). Furthermore, the root mean square errors (RMSE) of these three schemes in the most interesting region which is around the strike price, have been compared.
