Metode Beda Hingga dan Fast Fourier Transform pada Valuasi Opsi Call Eropa

Abstract

This study aims to apply and analyze the efficiency and accuracy of the Crank-Nicolson Finite Difference Method (FDM) and the Carr-Madan Fast Fourier Transform (FFT) in the valuation of European call options. A case study was conducted on 33 stocks that were consistently included in the LQ45 Index from September 2023 to August 2025. Accuracy was evaluated using the Relative Percentage Error (RPE) against the analytical Black-Scholes prices, while efficiency was measured based on computational time. The results indicate that both methods demonstrate a very high level of precision in replicating the Black-Scholes option values, with an average RPE of 0.15888% for the FDM and 1.63522×10^(-13)% for the FFT. Moreover, the FFT method proved to be significantly more efficient, requiring only 0.06 seconds of computational time for the entire sample, compared to the FDM which required 30.97 seconds. Based on these results, the FFT method demonstrates superior computational efficiency compared to the Crank–Nicolson FDM, while maintaining a very high degree of accuracy in replicating Black–Scholes option prices.