次分数环境下标的股票有分红和配股的亚式期权定价  

Asian Option Pricing on Dividend-Paying and Placing Stocks under Sub-Fractional Brownian Motion

作　　者：胡攀 HU Pan(Mathematics School of Sichuan University of Arts and Science,Dazhou Sichuan 635000,China)

机构地区：[1]四川文理学院数学学院,四川达州635000

出　　处：《乐山师范学院学报》2024年第4期8-14,共7页Journal of Leshan Normal University

基　　金：达州市社科联重点研究基地数学与金融研究中心一般项目“混合次分数环境下亚式期权定价”(SCMF202203);四川文理学院一流课程建设资助项目“概率论与数理统计”(2020KCB016)。

摘　　要：针对次分数环境下标的股票有连续分红且配、送股次数随机的几何平均亚式期权的定价问题,利用随机分析方法得到了几何平均亚式看涨、看跌期权的定价公式及其平价关系。数值模拟结果表明,几何平均亚式看涨、看跌期权的价格与配、送股比例,配股价和除权除息前股价呈不同的变化趋势,但均与Hurst指数成反比。该研究对丰富期权定价模型具有理论意义,同时为我国金融市场的期权投资者提供了参考依据。In order to solve the pricing problem of geometric average Asian options with continuous dividends and random allocation and delivery times under sub-fractional environment,the pricing formulas of geometric average Asian call and put options and their parity relations are obtained by using stochastic analysis method。The numerical simulation results show that the price of the geometric average Asian call and put options have different trends with the proportion of the allocation,the price of the allocation and the stock price before the right and ex-dividend,but all of them are inversely proportional to the Hurst index。This study has important theoretical significance for enriching the option pricing model,and provides an important theoretical reference for the option investors in China's financial market。

关 键 词：次分数布朗运动 连续分红 配股 几何平均亚式期权 数值模拟 

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