基于q-高斯过程下的带红利欧式期权定价  

Pricing of European option with dividend based on q-Gaussian process

作　　者：刘利敏[1] 闫钰蕾 Liu Limin;Yan Yulei(College of Mathematics and Information Science,Henan Normal University,Xinxiang 453007,China)

机构地区：[1]河南师范大学数学与信息科学学院,河南新乡453007

出　　处：《河南师范大学学报（自然科学版）》2023年第3期90-96,共7页Journal of Henan Normal University(Natural Science Edition)

基　　金：国家社科基金(18BJY247).

摘　　要：研究了q-高斯过程下带分红的欧式期权定价及参数估计问题.首先得到不同分红情形下的定价公式,对于按照红利率情形的分红问题,通过求解带分红的随机微分方程得到对应的欧式看涨期权的定价公式;对于离散分红的情形,通过构造套期保值策略,导出带有离散分红的期权定价公式.然后研究q-高斯过程中的参数估计问题.对于q,使用R/S分析法估计出Hurst指数H的值,再通过q与H之间的关系估计出q;采用矩估计得到μ,σ的估计量,并证明μ估计量的无偏性.最后进行模拟分析,并利用微软公司的股票价格以及期权价格进行实证分析.This paper studies the pricing and parameter estimation of European options with dividends under q-Gaussian process.Firstly,the pricing formulas of different dividend cases are obtained.For the dividend problem with red interest rate,the pricing formula of European call option is obtained by solving the stochastic differential equation with dividend.In the case of discrete dividend,the option pricing formula with discrete dividend is derived by constructing hedging strategy.The study of parameter estimation in Gauss process,for q,the value of Hurst index H is estimated by R/S analysis method,and then q is estimated by the relationship between q and H.The estimators ofμandσare obtained by moment estimation,and the unbiasedness ofμestimators is proved.Finally,the simulation analysis is carried out,and the stock price and option price of Microsoft are used for empirical analysis.

关 键 词：欧式期权 q-高斯过程 分红 参数估计 

分 类 号：O29[理学—应用数学]