混合双分数布朗运动下的永久美式回望期权定价  

Perpetual American lookback option pricing under mixed bi-fractional Brownian motion

作　　者：张亚茹 夏莉 张典秋[1] ZHANG Yaru;XIA Li;ZHANG Dianqiu(School of Statistics and Mathematics,Guangdong University of Finance and Economics,Guangzhou 510320,Guangdong,China;Big Data and Educational Statistics Application Laboratory,Guangdong University of Finance and Economics,Guangzhou 510320,Guangdong,China)

机构地区：[1]广东财经大学统计与数学学院,广东广州510320 [2]广东财经大学大数据与教育应用统计实验室,广东广州510320

出　　处：《山东大学学报（理学版）》2024年第4期98-107,共10页Journal of Shandong University(Natural Science)

基　　金：国家自然科学基金资助项目(11971200);广东省教育厅科研项目(2018KCXTD013);广东省教育厅科研项目[特色创新项目](2018KTSCX069);广东省教育厅委托项目(0835-210Z33606691)。

摘　　要：构建混合双分数布朗运动驱动下的带有红利的永久美式回望期权定价模型。首先,通过Δ-对冲原理,给出混合双分数布朗运动下的永久美式回望看涨和看跌期权所满足的偏微分方程组;其次,通过变量代换法、特征方程法对建立的偏微分方程组进行求解,给出混合双分数布朗运动下的永久美式回望看涨和看跌期权定价公式及其最佳实施边界;最后,通过数值实验,验证该解的线性等比例缩放性质,并讨论混合双分数布朗运动参数H、K及波动率对期权价格的影响。A pricing model for a perpetual American lookback option with dividends driven by mixed bi-fractional Brownian motion is constructed in this paper.First,the partial differential equations of mixed bi-fractional Brownian motion for perpetual American lookback call and put options are given by theΔ-hedging principle.Then,the established partial differential equations are solved by variable substitution method and characteristic equation method.Finally,numerical experiments are adopted to verify the linear proportional scaling properties of the solution,and the effects of mixed bi-fractional Brownian motion parameters H,K and volatility on the option prices are further discussed.

关 键 词：混合双分数布朗运动 永久美式回望期权 期权定价 

分 类 号：O211.6[理学—概率论与数理统计] F830.9[理学—数学]