分数布朗运动下带交易费用和红利的两值期权定价  

BINARY OPTION PRICING WITH TRANSACTION COSTS AND DIVIDENDS IN A FRACTIONAL BROWNIAN MOTION ENVIRONMENT

作　　者：韦才敏[1,2] 林先伟 范衠 WEI Cai-min;LIN Xian-wei;FAN Zhun(Department of Mathematics,Shantou University,Shantou 515063,China;Guangdong Provincial Key Lab of Digital Signals and Image Processing,Shantou University,Shantou 515063,China)

机构地区：[1]汕头大学数学系,广东汕头515063 [2]汕头大学数字信号与图像处理技术重点实验室,广东汕头515063

出　　处：《数学杂志》2018年第5期912-920,共9页Journal of Mathematics

基　　金：国家社会科学基金重点项目(16AGL010);国家自然科学基金项目(61175073);广东省自然科学基金项目(2017A030313005)

摘　　要：本文研究了在分数布朗运动环境下带交易费用和红利的两值期权定价问题.在标的资产服从几何分数布朗运动的情况下,利用分数It公式和无风险套利原理建立了分数布朗运动环境下带交易费用和红利的两值期权的定价模型.再通过用偏微分方程的方法进行求解此定价模型,得到了在分数布朗运动下带交易费用和红利的两值期权定价公式.所得结果推广了已有结论.This paper deals with the problem of pricing Binary option with transaction costs and dividends under the fractional Brownian motion.Suppose that the stock price follows geometric fractional Brownian motion,by using fractional It^o formula and no-arbitrage principle,we establish the binary option pricing model with transaction costs and dividends.The method of partial differential equation are used to solve this model,and then we get the pricing formula of the binary option with transaction costs and dividends in a fractional Brownian motion environment,which extends the previous conclusions.

关 键 词：两值期权 期权定价 无风险套利原则 交易成本 分数布朗运动 

分 类 号：F224.7[经济管理—国民经济] O211.63[理学—概率论与数理统计]