Numerical Pricing of European Stock Option Based on Black-Scholes Model Using Crank-Nicolson Method
Abstract
Accurate option pricing is an important issue in quantitative finance, especially in emerging financial markets, which are generally characterized by price volatility and limited historical data. This research evaluates the numerical performance of the classical Crank–Nicolson finite difference method in determining the price of European call options based on the Black–Scholes model using Indonesian stock market data. The Black–Scholes equation is discretized on a uniform spatial and temporal grid, and the numerical solution is verified by comparison with the Black–Scholes analytical solution as a mathematical reference. The numerical results show that the Crank–Nicolson method produces stable and convergent solutions, with a relative error of less than 1% at a sufficiently fine grid resolution. Furthermore, sensitivity analysis to volatility and temporal convergence tests demonstrate the consistency of the numerical solution's behavior to variations in the model's key parameters. These findings indicate that the Crank–Nicolson method provides a reliable numerical approach for evaluating European option pricing within the classical Black–Scholes framework under the analyzed market conditions.
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DOI: http://dx.doi.org/10.30829/zero.v10i1.28070
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