This study compares an explicit finite difference method without far-field boundary conditions with an implicit operator splitting method for the Black-Scholes (BS) model in European option pricing in accuracy and compution time. In the explicit method, through progressive domain reduction during time iteration, coupled with a Saulyev-type temporal discretization, the method achieves stability, enabling the application of larger time steps. Its advantages lie in speed, simplicity, and efficiency, particularly beneficial for nonlinear boundary profiles like power options. The results demonstrate that the explicit scheme without the need for far-field boundary conditions, offers significant CPU time savings when applied to power options. Furthermore, the accuracy of both approaches is found to be comparable across both option types.
