A Compact Difference Scheme for European Options Under Sub-diffusion Black-Scholes Model
DENG Yiyang
SUN Yudong
Abstract：To address the limitations of the traditional Black-Scholes(B-S)model in illiquid markets,the subdiffusive B-S model was used to portray the market dynamics more accurately.Initially,the basic concept of the subdiffusive B-S model was briefly introduced,and the partial differential equation for European call options within this model was provided.Subsequently,time was discretized by the model through the Caputo derivative and space was discretized using a 4-order compact difference scheme by the model,and a compact difference scheme with time(2-α)-order and spatial 4-order accuracy was constructed.Thereafter,the stability and convergence of the method were verified using Fourier analysis and mathematical induction.Finally,the numerical results were simulated using R language,and the impact of variable parameters on option prices was analyzed.The results indicated that the European option pricing under the subdiffusive B-S model using the compact difference method was reasonable and effective,and its feasibility was confirmed through numerical experiments.A reference for option pricing issue was provided by the establishment of this model.
Keywords：stabilityastringencyoption pricinggeometric Brownian motionCaputo derivative
Publication Date：2025-03-19
Online Publishing Date：2025-08-15(First online date of this platform, not the publication date of the document)
Pages：7( 119-125 )