跳跃扩散模型下不同标的资产算术平均的亚式期权定价  

Arithmetic Average Asian Option Pricing of Different Underlying Assets under Jump Diffusion Model

作　　者：江慧敏 JIANG Huimin(Wannan Medical College,College of Public Foundation,241000,Wuhu,Anhui,China)

机构地区：[1]皖南医学院公共基础学院,安徽芜湖241000

出　　处：《淮北师范大学学报（自然科学版）》2024年第1期33-37,共5页Journal of Huaibei Normal University：Natural Sciences

基　　金：国家自然科学基金项目(11801199);安徽省自然科学基金项目(1908085QA30);皖南医学院教育研究项目(2018jyxm45)。

摘　　要：针对算术平均型亚式期权进行定价,分别采用标的资产为零息债券、平均资产和股票3种不同形式给出其相应的定价公式。基于每一种资产所拥有的鞅测度,分别采用伊藤公式和费曼卡茨公式,给出算术平均的亚式期权所服从的偏微分方程与终值条件。通过数值模拟验证该方法的有效性,从而有助于将该定价公式应用到更广阔的金融市场中。Because of the complexity of arithmetic average Asian option pricing,its pricing method has attracted much attention.For arithmetic Asian option pricing under three different underlying assets like zero coupon bond,average asset and stock,the method is based on the martingale measure of each asset,the partial differential equation of the arithmetic average Asian option is given by ITO′formula and Feynmankatz formula,respectively,and the corresponding final value conditions are given for the differential equations.The effectiveness of the method are verified by numerical simulation,which is helpful to apply the pricing formula to a wider financial market with stronger adaptability.

关 键 词：亚式期权 跳跃扩散模型 数值模拟 

分 类 号：O211.63[理学—概率论与数理统计]