A semidiscretization scheme for european option pricing based on the black scholes model - Nur Annisa Mulia; Rudianto Artiono (Desimal: Jurnal Matematika, 2025)
The development of derivative instruments in modern financial markets has created a growing need for option pricing methods that are both accurate and easy to implement. This study aims to calculate the price of European call options using the Black-Scholes model through a semidiscretization numerical approach. The method used involves time transformation, discretization of space variables, and explicit Euler scheme iteration to obtain numerical solutions. This method is applied to real stock price data, and the numerical results are compared with the Black-Scholes analytical solution at various grid numbers. The results show that accuracy increases with the number of grids, and the relative error is very small when M is large enough, so that this method is capable of producing a numerical approximation that is consistent with the analytical solution. These findings also confirm the trade-off between efficiency and accuracy,but still show that semidiscretization can be a practical, fast, and flexible alternative when analytical solutions are difficult to use or when parameter changes need to be evaluated dynamically. This research contributes by showing that a simple numerical approach can still work effectively in real market conditions, making it a practical and efficient alternative for analysts who need fast and flexible calculations without the complexity of advanced numerical methods.