摘要
本文考虑次分数跳-扩散环境下最值期权的定价问题.最值期权作为一种重要的新型金融衍生产品,它是讨论两个或多个风险资产的最大值或最小值期权.为了更贴合标的资产价格变化的实际过程,首先建立次分数跳-扩散过程下的金融市场模型,得到标的资产价格所满足的随机微分方程,然后再利用随机分析理论及保险精算方法,从而得到次分数跳-扩散过程下最值期权的定价公式.此过程推广了最值期权模型,使应用更为广泛.研究结果表明,与标准布朗运动下的期权价格相比,次分数跳-扩散下期权价格要同时取决于到期日、Hurst参数和跳跃次数.
The pricing problem of the maximum or minimum option is consided in the sub-fractional jump-diffusion envi-ronment. As an important new financial derivative, the maximum or minimum option of two or more risky assets is discussed. In order to better fit the actual process of price change of the underlying asset, the financial market model under the sub-fractional jump-diffusion process is established firstly, and get stochastic differential equation satisfied by the underlying asset price. Then the price fonnula of the maximum or minimum option under the sub-fractional jump-diffusion process is given by the sub-fractional jump-diffusion stochastic analysis theory and actuarial approach. This process extends the maximum or minimum option model and makes it more widely used. The results show that compared with the price of option under standard Brownian motion , the option price under sub-fractional jump-diffusion depends on expiration, Hurst parameter and jump numbers.
作者
梁喜珠
薛红
王瑞
UANG Xizhu;XUE Hong;WANG Rui(School of Science, Xi’an Polytechnic University, Xi’an 710048,China)
出处
《四川理工学院学报（自然科学版）》
CAS
2019年第5期80-86,共7页
Journal of Sichuan University of Science & Engineering(Natural Science Edition)
基金
国家自然科学基金(11601410)
陕西省自然科学基础研究计划(2016JM1031)
中国博士后科学基金(2017M613169)
关键词
随机分析
次分数跳-扩散过程
最值期权
保险精算方法
期权定价
stochastic analysis
sub-fractional jump-diffusion process
minimum or maximum option
actuarial approach
option pricing
