Abstract
The Black-Scholes equations have been increasingly popular over the last three decades since they provide more practical information for optional behaviours. Therefore, effective methods have been needed to analyze these models. This study will focus mainly on investigating the behavior of the Black-Scholes equation for the European put option pricing model. To achieve this, numerical solutions of the Black-Scholes European option pricing model are produced by three combined methods. Spatial discretization of the Black-Scholes model is performed using a fourth-order finite difference (FD4) scheme that allows a highly accurate approximation of the solutions. For the time discretization, three numerical techniques are proposed: a strong-stability preserving Runge Kutta (SSPRK3), a fourth-order Runge Kutta (RK4) and a one-step method. The results produced by the combined methods have been compared with available literature and the exact solution.
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