次分数布朗运动下具有随机利率和跳跃风险的两值期权定价  

Pricing Binary Options with Stochastic Interest Rate and Jumps in Sub-fractional Brownian Motion

作　　者：程潘红 许志宏[3] CHENG Pan-hong;XU Zhi-hong(Business School,University of Shanghai for Science&Technology,Shanghai 200093,China;School of Mathematics and Finance,University of Chuzhou,Chuzhou 239000,Anhui,China;Public Teaching Department,Rizhao Polytechnic,Rizhao 276826,Shandong,China)

机构地区：[1]上海理工大学管理学院,上海200093 [2]滁州学院数学与金融学院,安徽滁州239000 [3]日照职业技术学院公共教学部,山东日照276826

出　　处：《内蒙古师范大学学报（自然科学版）》2022年第1期68-77,共10页Journal of Inner Mongolia Normal University(Natural Science Edition)

基　　金：安徽省高校自然科学重点研究资助项目(KJ2018A0429,KJ2017A426)。

摘　　要：金融资产的合理定价不仅能够提升金融市场的运行效率,也利于投资者在复杂多变的金融市场中做出有效决策使得自身收益最大化。考虑到金融资产价格的长记忆性、跳跃风险及利率的随机性,在假定无风险利率满足次分数Vasicek模型、股票价格遵循带跳的几何次分数布朗运动的条件下,构建了两值期权的定价模型。应用次分数布朗运动的It?公式、保险精算方法推导得到两值期权的定价表达式。根据定价模型进行数值模拟,说明了利率的随机性和标的资产面临的跳跃风险对两值期权的定价结果有显著影响,并进一步指出了两值期权价值关于执行价格、利率的长期均值和赫斯特指数等基本参数的变化特点。Reasonable pricing of financial assets can not only improve the operation efficiency of the financial market,but also help investors make effective decisions in the complex and changeable financial market and maximize their own returns.In light of the long memory of financial asset price,jump risk and the randomness of interest rate,the pricing model of binary options was constructed under the assumption that the risk-free interest rate satisfied the sub-fractional Vasicek model and the stock price followed the geometric sub-fractional Brownian motion with jumps.The Ito formula and properties of sub-fractional Brownian motion,as well as actuarial approach were used to derive the pricing formula of binary options.The numerical simulations showed that the randomness of interest rate and the jump risk to underlying assets had significant impacts on pricing binary options and revealed furthermore the changing characteristics of the value of binary options with respect to the strike price,the long-term mean value of interest rate and Hurst index.

关 键 词：次分数布朗运动 随机利率 跳跃风险 两值期权 保险精算方法 

分 类 号：O211.6[理学—概率论与数理统计] F830.9[理学—数学]