广义双曲模型下锁定期权的定价  

Pricing lockup options under generalized hyperbolic model

作　　者：何二倩 李翠香[1] HE Er-qian;LI Cui-xiang(Hebei Normal University,School of Mathematical Sciences,Shijiazhuang 050024,China)

机构地区：[1]河北师范大学数学科学学院,石家庄050024

出　　处：《哈尔滨商业大学学报（自然科学版）》2021年第5期620-626,共7页Journal of Harbin University of Commerce：Natural Sciences Edition

基　　金：国家自然科学基金(11571089);河北省教育厅重点基金(ZD2018065,ZD2019053);河北师范大学在读研究生创新能力培养资助项目(CXZZSS2021048)。

摘　　要：在资产价格过程服从指数广义双曲Levy过程的条件下讨论锁定期权的定价问题.利用Esscher变换的方法找出Esscher风险中性测度,并利用一些分析技巧证明了该风险中性测度的唯一性.利用风险中性定价原理和测度变换的方法,借助于分布函数与特征函数的关系推导出锁定看涨、看跌期权价格的解析表达式.利用Matlab R2016b软件给出了数值分析,并给出了锁定看涨、看跌期权价格与执行价格、锁定时间、资产价格之间的关系.The aim of this paper is to price lockup options under the condition that the underlying asset's price follows exponential generalized hyperbolic Levy processes.Found the Esscher risk-neutral measure by Esscher transform,and the uniqueness of this risk-neutral measure was proved by some analysis techniques.By using the risk-neutral pricing principle,measure transform,and the relationship between distribution function and characteristic function,obtained the analytical expression to the prices of put and call lockup options.At the end,the numerical analysis was given by using Matlab R2016b software,and the relationship between the lockup call and put option prices and the strike price,the lock time and the asset price was given.

关 键 词：广义双曲模型 锁定期权 测度变换 特征函数 风险中性测度 ESSCHER变换 

分 类 号：O211.6[理学—概率论与数理统计]