摘要
金融市场经常受到一些不确定因素的影响,使得亚式期权的定价具有模糊性,同时资产价格的变化具有长记忆性和“尖峰厚尾”的特征.本文将金融市场的长记忆性特征纳入到模糊环境下的亚式期权定价模型中,用分数布朗运动刻画资产价格的变化过程.通过引入三角直觉模糊数来刻画期权价格估计的不确定性,构建了在分数布朗运动的Black-Scholes模型下欧式几何平均亚式期权的定价模型,给出了亚式期权三角直觉模糊价格截集.并重点研究了长记忆性指标Hurst指数H对具有固定敲定价格的几何平均亚式期权的影响.通过数值实验对模型的灵敏性和稳健性进行了分析.结果表明:在模糊环境下考虑长记忆性特征所得到的欧式几何平均亚式期权定价模型更符合金融市场.
The financial market is often affected by some uncertain factors,which make the pricing of Asian options fuzzy,and the changes of asset prices have the characteristics of long memory and“peak and thick tail”.In this paper,the long memory characteristics of financial market are incorporated into the Asian option pricing model under fuzzy environment,and the fractional Brownian motion is used to describe the change process of asset prices.By introducing trigonometric intuitionistic fuzzy numbers to describe the uncertainty of option price estimation.The pricing model of European geometric mean Asian option under fractional Brownian motion black-Scholes model is constructed,and the triangular intuitionistic fuzzy price intercept set of Asian option is given.The influence of Hurst index H on geometric mean Asian option with fixed price is studied.The sensitivity and robustness of the model are analyzed by numerical experiments.The results show that the European geometric mean Asian option pricing model is more in line with the financial market.
作者
于涛
韦才敏
李傲霜
范衠
YU Tao;WEI Caimin;LI Aoshuang;FAN Zhun(Department of Mathematics,Shantou University,Shantou 515063,Guangdong,China;Guangdong Provincial Key Lab of Digital Signals and Image Processing,Shantou University,Shantou,515063,Guangdong,China)
出处
《汕头大学学报（自然科学版）》
2022年第3期22-34,共13页
Journal of Shantou University：Natural Science Edition
关键词
欧式几何平均亚式期权
三角直觉模糊数
长记忆性
分数布朗运动
European geometric mean Asian option
trigonometric intuitional fuzzy numbers
long memory
fractional Brownian motion
作者简介
于涛(1995—),男(汉族),山东德州人,硕士研究生,研究方向:期权定价.E-mail:2842374488@qq.com。
