分数维下基于分数阶导数模型的期权定价  

Option pricing based on fractional derivative model in fractional dimension

作　　者：宋丽娜 朱荻 SONG Li-na;ZHU Di(School of Data Science and Artificial Intelligence,Dongbei University of Finance and Economics,Dalian 116025,China)

机构地区：[1]东北财经大学数据科学与人工智能学院,辽宁大连116025

出　　处：《高校应用数学学报（A辑）》2022年第2期165-176,共12页Applied Mathematics A Journal of Chinese Universities(Ser.A)

基　　金：国家自然科学基金(71501031);辽宁省教育厅科学研究经费项目(LJKZ1040);东北财经大学科研项目(DUFE2020Y41)。

摘　　要：基于分数阶微积分,利用对冲技术建立时空分数阶期权定价方程.根据定价条件,将改进的解析技术与分数阶差分近似相结合建立半解析求解模式处理分数阶导数模型.并对欧式期权进行定价和应用分析,对美式期权的价值进行数值模拟.利用图解说明分数维度下,时间与空间分数阶导数的阶数,级数解的收敛控制参数,波动率对期权价值的影响.文中的工作对期权定价分数阶动力学建模的可行性和有效性进行解释和分析,力求为金融衍生品定价及其相关理论研究提供新的思路.Based on fractional calculus,the work establishes a space-time fractional option pricing equation by the hedging technique.According to the pricing conditions,the improved analytical technique is combined with fractional difference approximation to establish the semi-analytical solving model and deal with the fractional derivative model.The pricing and application analysis of European options are carried out and American option is numerically simulated.The influences of the orders of fractional derivatives in time and space,the convergence-control parameter of series solution,and volatility on option value are illustrated in fractional dimension.This work explains and analyzes the feasibility and effectiveness of fractional dynamic modeling of option pricing,and strives to provide a new train of thought for financial derivatives pricing and related theoretical researches.

关 键 词：分数阶微积分 期权定价 分数阶偏微分方程 半解析解 

分 类 号：F830.91[经济管理—金融学]