次分数布朗运动下具有随机波动率的欧式期权定价  

European option pricing with stochastic volatility in sub-fractional Brownian motion environment

作　　者：吴静敏 薛红[1] 贾亦佳 WU Jingmin;XUE Hong;JIA Yijia(School of Science,Xi’an Polytechnic University,Xi’an 710048,China)

机构地区：[1]西安工程大学理学院,陕西西安710048

出　　处：《纺织高校基础科学学报》2020年第3期86-93,共8页Basic Sciences Journal of Textile Universities

基　　金：国家自然科学基金(11601410);陕西省自然科学基础研究计划(2016JM1031);中国博士后科学基金(2017M613169)。

摘　　要：为了刻画实际金融资产价格的变化过程,解决资产收益率不具有独立平稳增量以及波动率随机性等问题,建立了考虑标的资产价格服从次分数布朗运动驱动的随机微分方程,波动率满足次分数布朗运动驱动的,且服从Ornstein-Uhlenback(O-U)过程的随机波动率模型。结合上证50ETF期权数据进行实证分析,运用蒙特卡洛法模拟计算欧式期权价格,并与其他模型下的欧式期权价格进行对比分析。结果表明,扩展的期权定价模型更加符合实际金融市场,改进传统期权定价模型在实际应用中的不足。In order to reflect the change process of the actual financial asset price,and solve the problem that the return rate has no independent and stationarity increace and the random volatility of the actual financial asset price series,and improve the shortcomings of the traditional option pricing model in practical applications.Considers that the asset price follows stochastic differential equations driven by sub-fractional Brownian motion,and the volatility satisfied the Ornstein-Uhlenback(O-U)process,Stochastic analysis theory and Monte Carlo method are used to study European option,the empirical analysis is discussed using the 50ETF option.The Monte Carlo method is used to simulate European option prices,and compared with the European option price in other models.The results show that extended model is more adapted to the real financial market.

关 键 词：次分数布朗运动 随机波动率 蒙特卡洛模拟 期权定价 参数估计 

分 类 号：F830[经济管理—金融学] O211[理学—概率论与数理统计]