湖北民族大学学报（自然科学版）2025，Vol.43Issue(1)：119-125,7.DOI:10.13501/j.cnki.42-1908/n.2025.03.010
次扩散Black-Scholes模型下欧式期权的一种紧致差分格式
A Compact Difference Scheme for European Options Under Sub-diffusion Black-Scholes Model
摘要
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.关键词
稳定性/收敛性/期权定价/几何布朗运动/Caputo导数Key words
stability/astringency/option pricing/geometric Brownian motion/Caputo derivative分类
数理科学引用本文复制引用
邓乙阳,孙玉东..次扩散Black-Scholes模型下欧式期权的一种紧致差分格式[J].湖北民族大学学报（自然科学版）,2025,43(1):119-125,7.基金项目
贵州省教育厅青年科技人才成长项目(黔教合KY字[2016]168). （黔教合KY字[2016]168）
