次分数布朗运动下支付红利的欧式期权定价  

Pricing of European Option in Sub-factional Brownian Motion with Dividend Payments

作　　者：程志勇 郭精军 张亚芳 CHENG ZhiYong;GUO JingJun;ZHANG YaFang(School of Statistics,Lanzhou University of Finance and Economics,Lanzhou,730020,China;Reserch Center of Quantitative Analysis of Gansu Economic Development,Lanzhou University of Finance and Economics,Lanzhou,730020,China)

机构地区：[1]兰州财经大学统计学院,兰州730020 [2]兰州财经大学甘肃经济发展数量分析研究中心,兰州730020

出　　处：《应用概率统计》2018年第1期37-48,共12页Chinese Journal of Applied Probability and Statistics

基　　金：国家自然科学基金项目(批准号:71561017)、甘肃省自然科学基金项目(批准号:145RJZA033)和甘肃经济发展数量分析研究中心项目(批准号:SLYB201202)资助.

摘　　要：本文主要建立了次分数布朗运动下的期权定价模型,并且考虑了支付连续红利的情形.首先利用Wick-It?积分和偏微分方法得到了期权价格所满足的偏微分方程,然后经过变量替换转化为Cauchy问题,从而得到了支付红利的次分数布朗运动环境下的欧式看涨期权定价公式,相应地根据看涨看跌定价公式,得出欧式看跌期权定价公式.最后,对定价模型中的参数进行估计,并讨论了估计量的无偏性和强收敛性.In this paper,we establish the option pricing model under sub-fractional Brownian motion,and consider the situation of the continuous dividend payments.Firstly,Wick-Ito integral and partial differential method are used to get the option price of partial differential equation,and then through variable substitution into Cauchy problem,we can get the pricing formula of European call option with dividend-paying in sub-fractional Brownian motion environment.According to the pricing formula of European call option,the European put option pricing formula is obtained.Moreover,we study the parameter estimation in the model,and consider the unbiasedness and the strong convergence of the estimator.

关 键 词：次分数布朗运动 支付红利 期权定价 参数估计 

分 类 号：O212.6[理学—概率论与数理统计]