次分数布朗运动下具有随机波动率和跳过程期权定价模型  

Option Pricing Model with Stochastic Volatility and Jump Process in the Sub-Fractional Brownian Motion Envirenment

作　　者：吴静敏 薛红[1] 刘欣 WU Jingmin;XUE Hong;LIU Xin(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,西安710048

出　　处：《内蒙古大学学报（自然科学版）》2020年第6期585-592,共8页Journal of Inner Mongolia University：Natural Science Edition

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：在次分数布朗运动、随机波动过程服从几何布朗运动和Poisson跳扩散模型的已有研究基础上,对传统期权定价模型进行改进和拓展,综合考虑了金融资产价格变动非Markov性、随机波动率效应和"跳"风险,建立次分数布朗运动环境下具有随机波动率与跳过程的欧式期权定价模型。给出模型的参数估计,并进行实证分析,采用蒙特卡罗方法模拟欧式期权价格。通过与其它模型对比说明提出的模型更符合金融市场实际情况,对于期权定价金融研究具有一定的理论意义。We improve and extend the traditional option pricing model on the basis of sub-fractional Brownian motion,the stochastic fluctuation process obeying geometric Brownian motion and Poisson jump-diffusion model.Considering the non-Markov property and the stochastic volatility and the jumps of financial asset prices,the stock price model with the stochastic volatility and jump process in the sub-fractional Brownian motion environment is built.We give the parameter estimates of the model and conduct empirical analysis,and use Monte Carlo to simulate European option prices.The comparison with other models shows that the proposed model is more in line with the actual conditions of the financial market,and has certain theoretical significance for the financial research on option pricing.

关 键 词：次分数布朗运动 随机波动率 POISSON过程 参数估计 蒙特卡洛模拟 

分 类 号：O211[理学—概率论与数理统计] F830[理学—数学]