随机波动率反馈效应和杠杆效应的研究  

The Impact of Leverage and Volatility Feedback Effect Based on Stochastic Volatility Model

作　　者：江良[1] 林琦 张新军[3] JIANG Liang;LIN Qi;ZHANG Xin-jun(Fujian Key Laboratory of Financial Information Processing,Putian University,Putian 351100,China;Key Laboratory of Financial Mathematics of Fujian Province University,Putian University,Putian 351100,China;Key Laboratory of Applied Mathematics of Fujian Province University,Putian University,Putian 351100,China)

机构地区：[1]福建省金融信息处理重点实验室莆田学院,福建莆田351100 [2]金融数学福建省高校重点实验室莆田学院,福建莆田351100 [3]应用数学福建省高校重点实验室莆田学院,福建莆田351100

出　　处：《数学的实践与认识》2023年第8期146-154,共9页Mathematics in Practice and Theory

基　　金：福建省自然科学基金(2020J01907,2021J011102);福建省社会科学基金(FJ2018B065)。

摘　　要：在随机波动率模型基础上研究波动率反馈效应和杠杆效应,前者定义为在漂移项中引入波动率项,后者通过滞后收益和波动率负的相关性来描述.借鉴于微分算子展开技巧计算精确的矩函数,进一步应用广义矩方法给出模型的参数估计值和统计推断.基于上证综合指数市场数据,实证结果揭示了具有波动率反馈和杠杠效应的模型改善了似然值.此外,实证结果也表明了波动率反馈效应加强了杠杆效应.This paper incorporates volatility effect and leverage feedback into the stochastic model,The former is described by defining the linear relationship between the contemporaneous returns and the volatilities,and the latter is defined as the negative correlation between the lagged returns and the current volatilities.We apply the expansion of the differential operator to compute the closed-form moment functions,and further develop the general moment method to estimate the parameters in the model and make statistical inference.The empirical results show that the model with volatility feedback effect can improve the likelihood ratio.In addition,the empirical results also support that the volatility feedback effect strengthens the impact of the leverage effect.

关 键 词：随机波动率 杠杆效应 波动率反馈效应 

分 类 号：O213[理学—概率论与数理统计] F832.51[理学—数学]