混合分数布朗运动下欧式期权模糊定价研究  

Fuzzy Pricing of European option Based on Mixed Fractional Brownian Motion

作　　者：林先伟 秦学志[1] 尚勤[1] LIN Xian-wei;QIN Xue-zhi;SHANG Qin(School of Economics and Management,Dalian University of Technology,Dalian 116024,China)

机构地区：[1]大连理工大学经济管理学院,辽宁大连116024

出　　处：《运筹与管理》2022年第7期173-178,共6页Operations Research and Management Science

基　　金：国家自然科学基金资助项目(71471026,71871040);国家自然科学基金重点项目(71731003);国家社科基金重大项目(18ZDA095);国家社科基金资助项目(19BJY228);辽宁省“兴辽英才计划”哲学社会科学领军人才项目(XLYC1804005);辽宁省社会科学规划基金(L16BGL012)。

摘　　要：本文采用混合分数布朗运动来刻画标的股票价格的动态变化,以此体现金融市场的长记忆性特征。在混合分数Black-Scholes模型的基础上,基于标的股票价格、无风险利率和波动率均是模糊数的假定下,构建了欧式期权模糊定价模型。其次,分析了金融市场长记忆性的度量指标Hurst指数H对欧式期权模糊定价模型的影响。最后,数值实验表明:考虑长记忆性特征得到的欧式期权模糊定价模型更符合实际。In this paper,the mixed fractional Brownian motion is used to describe the dynamic change of the underlying stock price,so as to capture the long-term memory property of the financial market.On the basis of mixed fractional Black-Scholes model,assuming that the underlying stock price,risk-free interest rate and volatility are all fuzzy numbers,a fuzzy pricing model of European options based on mixed fractional Brownian motion is established.Secondly,the influence of Hurst index H,a measure of long-term memory in financial market,on European option pricing is analyzed.Finally,the numerical experimental results show that the fuzzy pricing model of European options based on long memory is more practical.

关 键 词：欧式期权 混合分数布朗运动 模糊数 期权定价 

分 类 号：F830.9[经济管理—金融学]