次分数布朗运动下具有固定敲定价格的几何平均亚式期权定价  

Option Pricing of Geometric Average Asian Options with Fixed Strike Price in Sub-fractional Brownian Motion

作　　者：王春雨 郭志东 WANG Chunyu;GUO Zhidong(School of Mathematics and Physics,Anqing Normal University,Anqing 246133,China)

机构地区：[1]安庆师范大学数理学院,安徽安庆246133

出　　处：《湖北民族大学学报（自然科学版）》2023年第2期275-280,共6页Journal of Hubei Minzu University:Natural Science Edition

基　　金：安徽省自然科学青年基金项目(1908085QA29)。

摘　　要：建立了次分数布朗运动机制下具有固定敲定价格的几何平均亚式期权定价模型。运用Δ对冲技巧和Ito公式得到了几何平均亚式看涨期权在次分数机制下的偏微分方程。进一步求解偏微分方程的定解问题,得到了具有固定敲定价格的几何平均亚式看涨期权的定价公式及看涨、看跌期权间的平价公式。数值计算结果表明,随着Hurst参数的增大,具有固定敲定价格的几何平均亚式看涨期权的价格将减小;另外,具有固定敲定价格的几何平均亚式看涨期权在次分数机制下的价格要低于其在经典布朗运动下的价格。The pricing model of geometric average Asian options with fixed strike price is constructed under the sub-fractional Brownian motion regime.The partial differential equation for the geometric average Asian options with fixed strike price under sub-fractional mechanism is obtained by usingΔhedging technique and Itoformula.Furthermore,by solving the definite solution problem of partial differential equation,the pricing formula of geometric average Asian call option with fixed strike price and the call-put parity formula are given.The numerical results show that with the increase of Hurst parameter,the price of geometric average Asian call option with fixed strike price will decrease.It is also shown that the price of geometric average Asian call option with fixed strike price under sub-fractional mechanism is lower than that under classical Brownian motion.

关 键 词：次分数布朗运动 几何平均亚式期权 固定敲定价格 ITO公式 Δ对冲技巧 

分 类 号：F830.9[经济管理—金融学]