混合双分数布朗运动下的几何平均亚式期权定价  

Geometric Mean Asian Option Pricing Driven by Mixed Double Fractional Brownian Motion

作　　者：李悦 康元宝 秦文静 LI Yue;KANG Yuanbao;QIN Wenjing(School of Mathematical Sciences,Chongqing Normal University,Chongqing 401331,China)

机构地区：[1]重庆师范大学数学科学学院,重庆401331

出　　处：《东莞理工学院学报》2025年第1期26-34,共9页Journal of Dongguan University of Technology

基　　金：重庆市自然科学基金(cstc2019jcyj-msxmX0146)。

摘　　要：用混合双分数布朗运动来刻画标的资产价格变化,建立几何平均亚式期权的数学模型。运用混合双分数布朗运动的Ito公式,得到标的资产价格的显示解。由泰勒展开式以及Δ对冲原理得到几何平均看涨期权的偏微分方程,利用变量代换将方程降维,利用热传导方程经典理论从而得到在t时刻,具有固定敲定价格的几何平均亚式看涨期权的价格。In this paper,the mixed double fractional Brownian motion is used to describe the price change of the underlying asset,so as to establish the mathematical model of geometric mean Asian options.Using the Ito formula of mixed fractional Brownian motion,this article obtains the explicit solution of the underlying asset price.The partial differential equation of geometric average call options is obtained from Taylor expansion andΔhedging principle.The equation is reduced in dimension by variable substitution,and the classical theory of heat conduction equation is used to obtain the value of geometric average Asian call options with fixed strike prices at time t.

关 键 词：混合双分数布朗运动 Δ对冲原理 热传导方程经典理论 几何平均亚式期权 

分 类 号：O211[理学—概率论与数理统计]