均值回复跳扩散随机波动率模型下的欧式期权定价研究  

European Option Pricing under the Log Mean-Reverting Jump Diffusion Stochastic Volatility Model

作　　者：马爱琴 郭精军 汪育兵 张翠芸 MA AIQIN;GUO JINGJUN;WANG YUBING;ZHANG CUIYUN(School of Statistics and Data Science,Lanzhou University of Finance and Economics,Lanzhou 730020,China;Centre for Quantitative Analysis of Gansu Economic Development,Lanzhou University of Finance and Economics,Lanzhou 730020,China)

机构地区：[1]兰州财经大学统计与数据科学学院,兰州730020 [2]兰州财经大学甘肃经济发展数量分析研究中心,兰州730020

出　　处：《应用数学学报》2024年第2期333-354,共22页Acta Mathematicae Applicatae Sinica

基　　金：国家自然科学基金项目(71961013,72361016);甘肃省教育厅“双一流”科研重点项目(GSSYLXM-06);甘肃省2024年省级人才重点项目资助。

摘　　要：考虑到金融市场数据波动的不确定性,本文提出了一个新的对数均值回复跳扩散4/2随机波动率(LMRJ-4/2-SV)模型.首先,构建了LMRJ-4/2-SV模型,并利用FFT等方法获得了基于LMRJ-4/2-SV模型的欧式期权定价公式.其次,对实际市场数据进行描述性统计分析,探讨标的资产价格变化特征及LMRJ-4/2-SV模型的适用性,并通过粒子群优化算法估计模型参数.最后,基于LMRJ-4/2-SV模型下的期权定价公式及模型参数估计值对欧式期权进行定价,并将其定价结果与4/2、3/2、Heston模型估计值及市场价格进行对比.结果表明:基于LMRJ-4/2-SV模型的欧式期权定价误差最小,定价结果较其它随机波动率模型而言具有明显优势.Considering the uncertainty of financial market data volatility,a new log-mean reversion jump diffusion 4/2 random volatility(LMRJ-4/2-SV)model was pro-posed in this paper.Firstly,the LMRJ-4/2-SV model was constructed,and the Euro-pean option pricing formula based on LMRJ-4/2-SV model was obtained by using FFT and other methods.Secondly,descriptive statistical analysis of the actual market data was carried out to discuss the price change characteristics of the underlying asset and the applicability of the LMRJ-4/2-SV model,and the model parameters were estimated by particle swarm optimization algorithm.Finally,European options were priced based on the option pricing formula and parameter estimates under the LMRJ-4/2-SV model,and the pricing results were compared with the 4/2,3/2,Heston model estimates and market prices.The results show that the pricing error of European option based on LMRJ-4/2-SV model is minimal,and the pricing results have obvious advantages over other stochastic volatility models.

关 键 词：对数均值回复 期权定价 跳扩散 随机波动 

分 类 号：O211.63[理学—概率论与数理统计]