两类蝶式期权方差和协方差的半参数界  

Semiparametric bounds of variance and covariance for two kinds of butterfly options

作　　者：艾晓辉[1] 刘宗昊 白瑞杰 王茹雪 AI Xiaohui;LIU Zonghao;BAI Ruijie;WANG Ruxue(School of Science,Northeast Forestry University,Harbin,Heilongjiang 150040,China)

机构地区：[1]东北林业大学理学院,黑龙江哈尔滨150040

出　　处：《石河子大学学报（自然科学版）》2023年第5期633-639,共7页Journal of Shihezi University(Natural Science)

基　　金：黑龙江省博士后资助项目(LBH-Q21059);东北林业大学2021年度大学生创新创业训练计划项目(202110225124)。

摘　　要：本文的目的是在已知随机变量某些矩信息的条件下,给出随机变量函数的方差和相应协方差的半参数界。本文应用对偶原理,给出了美式蝶式期权和欧式蝶式期权的方差的上界估计。运用等价公式,测度变换,找到控制函数,分别给出了单峰分布下欧式看涨期权与美式蝶式期权的协方差的下界估计以及欧式看涨期权与欧式蝶式期权的协方差的上界估计。The purpose of the research is to give the semiparametric bounds of the variance and the corresponding covariance of the function of the random variable,when some moment information of the random variable is given.Through the principle of duality the upper bound estimates of the variance of American butterfly options and European butterfly options are given.Using the equivalent for-mula and measure transformation,we find the control function,and give the lower bound estimation of the covariance of European call option and American butterfly option under unimodal distribution and the upper bound estimation of the covariance of European call op-tion and European butterfly option.

关 键 词：对偶原理 测度变换 单峰分布 半参数界 

分 类 号：O211.5[理学—概率论与数理统计]