基于MFBM模型对亚式期权模拟定价的研究  

Research on Asian Option Simulation Pricing Based on MFBM Model

作　　者：陈敦勇 孙玉东 CHEN Dunyong;SUN Yudong(School of Data Science and Information Engineering,Guizhou Minzu University,Guiyang 550025,China;Business School,Guizhou Minzu University,Guiyang 550025,China)

机构地区：[1]贵州民族大学数据科学与信息工程学院,贵阳550025 [2]贵州民族大学商学院,贵阳550025

出　　处：《湖北民族大学学报（自然科学版）》2023年第3期397-404,共8页Journal of Hubei Minzu University:Natural Science Edition

基　　金：贵州省科学技术基金项目([2015]2076)。

摘　　要：为了对两资产亚式看涨期权模拟定价问题展开研究,提出基于混合分数布朗运动(mixed fractional Brownian motion,MFBM)模型。首先,基于无套利原理,构造出包含2个自变量的偏微分方程;其次,使用变量变换,对微分方程进行证明并给出其解析解;最后,通过R语言模拟给出数值结果,并分析了Hurst指数、波动率等参数对期权价格的影响。结果表明,在混合分数布朗运动环境下所构造的偏微分方程对亚式期权的定价合理且有效,该模型的建立为多资产期权的定价问题提供了参考。In order to study the simulation pricing of two-asset Asian call options,the mixed fractional Brownian motion(MFBM)is proposed.Firstly,based on the principle of no arbitrage,a partial differential equation containing two independent variables is constructed.Secondly,the differential equation is proved by variable transformation and its analytical solution is given.Finally,numerical results are given through R language simulation,and the influences of Hurst index,volatility parameters and other parameters on option prices are analyzed.The results show that the partial differential equation constructed under mixed fractional Brownian motion is reasonable and effective for the pricing of Asian options.The establishment of this model provides a reference for the pricing of multi-asset options.

关 键 词：标准布朗运动 无套利原理 混合分数布朗运动 HURST指数 数值模拟 

分 类 号：F830.9[经济管理—金融学] O241.82[理学—计算数学]