Crank-Nicolson Finite Difference Pricing of European Call Options under the Black-Scholes Model
Abstract
This study aims to determine the price of European call options using the Crank–Nicolson finite difference method in the Black–Scholes model with stock data from XYZ Company for the period January 2025 to December 2025. Annual volatility is calculated based on historical closing price data, while numerical option prices are obtained through the Crank–Nicolson finite difference scheme and compared it with the Black–Scholes analytical solution as a reference. The results show that the Crank–Nicolson method produces a call option price of 596.08, while the Black–Scholes analytical solution gives a value of 612.50. The relative difference between the two methods is 2.68%, which indicates a good level of accuracy for the numerical method used. These findings indicate that the Crank–Nicolson finite difference method is capable of providing a stable and accurate numerical approach to determining the price of European call options. In practical terms, the results of this study contribute to the application of numerical-based option pricing models in emerging markets, particularly in conditions of dynamic volatility, where analytical approaches may have limitations in implementation
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DOI: http://dx.doi.org/10.30829/zero.v10i1.28482
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