Numerical analysis of fractional order Black-Scholes option pricing model with band equation method (Q6581976)

The novelty of this research lies in introducing a novel approach employing band matrix equations for numerically solving the fractional order Black-Scholes option pricing model. The authors explore the numerical solutions for fractional European options using three distinct methods: Laplace transform, Hilbert transform, and Monte Carlo simulation. Each method's convergence is rigorously proven, and their respective convergence orders are derived. A comprehensive analysis to discern the factors influencing the convergence rates for each method is discussed. Additionally, the authors observe the effectiveness and efficiency of the proposed methods in solving fractional European options through numerical examples.\N\NThis research contributes significantly to the comprehension of fractional European option pricing and provides valuable guidance for both practitioners and researchers in selecting the most suitable method for pricing these intricate financial instruments. In Section 6, the authors present three numerical examples. First, a comparative and analytical study of these three methods is conducted. Second, a comparison analysis of model parameters is performed. Next, a comparison with the exact solution of the SDE driven by fractional Brownian motion is made.