Examination of Impact from Different Boundary Conditions on the 2D Black-Scholes Model : Evaluating Pricing of European Call Options

Abstract: This paper examines different combinations of close-field and far-field boundary conditions for solving the 2D Black-Scholes model using finite difference methods in space. The combinations were also tested for different parameter settings. The research showed that in the area close to the strike price, the error was not particularly affected by the boundary conditions but rather by the characteristics of the problem itself. The main differences in error for the combinations of conditions are located close to the boundaries. However, if the computational domain for some reason has to be reduced, e.g. to save computational time, the boundary conditions will play an important role on the error in the area close to the strike price. Based on the findings presented in this report, Dirichlet boundary condition on the far- field boundary together with no boundary condition on the close-field is the best combination. If any of those are not applicable, the linearity condition should be used on that boundary instead.