基于调和稳态均值回复模型的VIX期权定价  

VIX option pricing based on mean reverting models with tempered stable processes

作　　者：尹亚华 吴恒煜[3] 朱福敏[4] Yin Yahua;Wu Hengyu;Zhu Fumin(School of Economic Information Engineering,Southwestern University of Finance and Economics,Chengdu 611130,China;Sichuan Provincial Key Laboratory of Financial Intelligence and Financial Engineering,Southwestern University of Finance and Economics,Chengdu 611130,China;School of Management,Jinan University,Guangzhou 510632,China;College of Economics,Shenzhen University,Shenzhen 518060,China)

机构地区：[1]西南财经大学经济信息工程学院,四川成都611130 [2]西南财经大学金融智能与金融工程重点实验室,四川成都611130 [3]暨南大学管理学院,广东广州510632 [4]深圳大学经济学院,广东深圳518060

出　　处：《系统工程学报》2021年第5期653-667,共15页Journal of Systems Engineering

基　　金：国家自然科学基金资助项目(72071132,71790615,72173089);中国博士后科学基金资助项目(2021M692168).

摘　　要：为有效地刻画VIX的均值回复性与非高斯性,在风险中性测度下,以调和稳态过程替换简单跳过程,构建带调和稳态的OU与CIR模型,并应用Doob鞅的方法求解其仿射解结构的特征函数,进而求出VIX期权公式用于定价实证.实证表明:带调和稳态的均值回复模型明显优于其他定价模型,而带调和稳态的CIR模型为最优定价模型.从而得出带调和稳态的均值回复模型不仅有较好的经济解释,而且可抓住VIX均值回复与非对称跳的特征,降低VIX期权定价的误差的结论.In order to effectively characterize the mean reverting and non-Gaussianity of VIX,using the risk neutral measure,this paper replaces the simple jump process with the tempered stable processes,constructs the OU model and CIR model with the tempered stable processes,and applies the Doob martingale method to solve the characteristic function of its affine solution structure,and then the VIX option pricing formula is obtained for empirical pricing.The empirical results show that the mean reverting model with tempered stable processes is significantly better than other pricing models,and the CIR model with tempered stable process is the optimal pricing model in this paper.Therefore,it is concluded that the mean reverting model with tempered stable processes not only has a good economic explanation,but also can capture the characteristics of VIX mean reverting and asymmetric jump,thereby reducing the error of VIX option pricing.

关 键 词：均值回复模型 非对称跳 调和稳态 VIX期权定价 

分 类 号：F830[经济管理—金融学]