Lévy过程驱动非高斯OU随机波动率下的期权定价  

Option pricing in non-Gaussian Ornstein-Uhlenbeck stochastic volatility processes driven by the Lévy process

作　　者：刘志东[1] 刘雯宇[1] 阮禹铭 LIU Zhi-dong;LIU Wen-yu;RUAN Yu-ming(School of Management Science and Engineering,Central University of Finance and Economics,Beijing 100081,China)

机构地区：[1]中央财经大学管理科学与工程学院,北京100081

出　　处：《管理科学学报》2019年第1期17-43,共27页Journal of Management Sciences in China

基　　金：国家自然科学基金资助项目(71271223; 70971145);教育部新世纪优秀人才支持计划资助项目(NCET-13-1054);中央财经大学青年创新团队项目;中央财经大学博士研究生重点选题支持计划

摘　　要：考虑金融时间序列发生的跳跃、随机波动率和"杠杆效应",建立由不同Lévy过程驱动的非高斯OU随机波动模型.通过结构保持等价鞅测度变换和FFT技术,对不同Lévy过程驱动下的非高斯OU(non-Gaussian Ornstein-Uhlenbeck process)期权定价问题进行研究.同时,在结构保持等价鞅测度下,推导出不同Lévy过程驱动下BNS模型离散化表达形式,并构建了基于SMC(sequential Monte Carlo)的极大似然估计、联合样本估计、梯度-SMC估计的非高斯OU期权定价模型参数估计方法.实证研究中,采用近470万个S&P500期权价格数据,从样本内拟合效果、样本外预测、模型稳定性、综合矫正风险几个方面,对不同Lévy过程驱动的非高斯OU期权定价模型、参数估计方法以及期权定价效果进行全面系统研究.实证研究表明,所有模型对实值期权的定价效果要优于虚值期权.本文基于联合样本估计和梯度-SMC估计的非高斯OU期权定价模型具有明显的优势.Based on the well-known(empirical) stylized facts such as infinite activity Lévy jump,stochastic volatility and leverage effect,this paper extends non-Gaussian OU stochastic volatility model,which is proposed by Barndorff-Nielsen and Shephard,driven by infinite activity Lévy jump processes.Then the European option pricing model is studied by FFT technology and the principle of structure preserving martingale measure the specific expressions of BNS models driven by different Lévy processes(Gaussian process,Gamma process and CGMY process) under the risk neutral measures are obtained.Efficient MLE-SMC algorithm,joint sample estimation algorithm and gradient-SMC algorithm are given to estimate the parameters and latent variables of non-Gaussian OU stochastic volatility models using stock and option prices.Finally,in contrast to most existing studies,our model assessment—an empirical research based on the 4.7 million price data of S&P500 options—is not restricted to the fitting performance,but even takes into account factors like model stability,the exposure to risks arising from the model calibration and the ability to explain observed prices of options.The empirical results show that the pricing effect of in-the-money options is superior to that of the out-of-the-money options.In most cases,the pricing effects of our BNS option pricing models based on joint sample estimation algorithm and gradient-SMC algorithm are better than that of MLE-SMC algorithm.

关 键 词：Lévy跳跃过程 非高斯OU过程 结构保持等价鞅测度 梯度序贯蒙特卡洛 期权定价 

分 类 号：F830[经济管理—金融学]