This study compares two finite difference schemes to solve the Black-Scholes (BS) model for option pricing. The explicit scheme with eliminating the need for far-field boundary conditions, through progressive domain reduction during time iteration coupled with a Saul’yev type temporal discretization. This method achieves stability, enabling the application of larger time steps. Its advantages lie in simplicity and efficiency particularly beneficial for nonlinear boundary profiles. The second one is an implicit finite difference scheme with operator splitting method. These two schemes have been compared for speed and accuracy in pricing several multi-asset European options. Standard computational tests demonstrate their performances for different options.
