基于非对称跳跃粗糙随机波动率模型的期权定价研究  

The pricing of SSE 50 ETF options based on asymmetric jump rough stochastic volatility model

作　　者：柳向东[1] 洪绍鹏 LIU Xiangdong;HONG Shaopeng(Department of Statistics and Data Sciences,School of Economics,Jinan University,Guangzhou 510632,China)

机构地区：[1]暨南大学经济学院统计与数据科学系,广州510632

出　　处：《系统工程理论与实践》2023年第2期350-370,共21页Systems Engineering-Theory & Practice

基　　金：国家自然科学基金(71471075);中央高校基本科研业务费专项资金(19JNLH09);教育部科技发展中心产学研创新基金重点项目(2019J01017);广东省重点平台及科研项目立项省创新团队项目(2016WCXTD004)。

摘　　要：基于资产价格存在的非对称跳跃与资产波动率存在的粗糙特性,本文提出了粗糙带非对称跳Heston模型(rHeston-AEDJ),在风险中性测度中推导出该模型的特征函数.由于模型的非马尔可夫且非半鞅性质,不能使用传统的欧拉方法进行逼近,本文使用混合模拟方法对该模型进行逼近,并解决粗糙波动率下奇异期权的定价问题.在风险中性测度下,基于Fourier-SINC推导了欧式期权的拟闭解.实证研究结果表明,上证50ETF价格存在跳跃、波动率Hurst指数远小于1/2,即波动率存在粗糙性,并基于拟闭解对上证50ETF期权进行定价实验发现本文所提出的rHeston-AEDJ模型在样本内外均有较好的定价精度.本文的研究对国内外期权产品定价与精确风险管理具有重要的现实意义和应用价值.Based on the asymmetric jumps in asset prices and the rough in the asset volatility,this paper proposesthe the rough Heston model with asymmetric jump(rHeston-AEDJ)and derives the characteristic functions in the risk-neutral measure.Due to the non-Markovian and non-semimartingale of the model,it cannot be approximated using the Euler method.A hybrid simulation approach is used to approximate the rough Heston model with asymmetric jump and can solve the pricing problem of exotic options under rough volatility with poisson jump.Under the risk-neutral measure,the quasi-closed function of the Euclidean option is derived based on Fourier-SINC.The results of the empirical study show that there is a jump in the price of Shanghai Stock Exchange(SSE)50 exchange traded fund(ETF)and the volatility Hurst index is much less than 1/2,i.e.,there is roughness in the volatility.The pricing experiment of SSE 50 ETF options based on the quasi-closed function finds that the proposed rHeston-AEDJ model has good pricing accuracy both inside and outside the sample.The findings of the study are of great practical significance and application value to the pricing and accurate risk management of domestic and foreign option products.

关 键 词：粗糙波动率模型 非对称指数分布 复合泊松跳跃 Fourier-SINC 上证50ETF期权定价 

分 类 号：F810.91[经济管理—财政学]