基于修正的已实现阈值幂变差的股市跳跃波动行为研究

基于非参数统计方法,利用考虑金融资产价格跳跃和杠杆效应的时点波动估计方法修正已实现阈值幂变差,构造甄别跳跃的检验统计量,对金融资产价格中的随机波动、有限活跃跳跃和无限活跃跳跃等问题进行综合研究。为同时吸收波动率的异方差集聚效应和收益率的非对称效应,对原有的已实现波动率异质自回归预测模型进行拓展,将非对称的异质性自回归模型的误差项设定为GARCH模型,以考察跳跃波动序列与连续波动序列之间的复杂关系。利用沪深股指高频数据进行实证研究,包括进行跳跃识别,跳跃活动程度检验和波动率预测效果对比。研究结果表明,沪深股市同时存在布朗运动成分、有限活跃跳跃和无限活跃跳跃成分,其中连续路径方差占主体。同时,收益和波动间的杠杆效应显著,无论短期还是长期,连续波动和跳跃波动对波动率的预测均具有显著影响,同时考虑股价的跳跃、波动和杠杆效应因素有助于更准确地刻画资产价格动态过程。

Research on Stock Market Jump and Volatility Dynamics Based on Modified Realized Threshold Power Variance

Based on the nonparametric statistical method, this paper uses the spot volatility estimation method of financial asset prices that cover jumps and leverage effects to modify the realized threshold power variation, and construct the test statistic of jumps. The issues of stochastic volatility in financial asset prices, finite activity jumps and infinite activity jumps are studied comprehensively. In order to incorporate the heteroskedasticity properties and clustering effects of volatility as well as asymmetric effects of returns, the original heterogeneous autoregressive forecasting model for realized volatility is extended and the error term of the asymmetric heterogeneous autoregressive model is set as the GARCH model so as to examine the complex relationships between the jump series and the continuous volatility series. This paper uses the high frequency data of Shanghai and Shenzhen stock indexes to conduct empirical researches, which include jumps recognition, the degree of jump activity test and volatility prediction. The results show that there are both Brownian motion components, finite active jump and infinite active jump components in Shanghai and Shenzhen stock markets, and the continuous path variance is dominant. At the same time, the leverage effects between returns and volatility is significant. Both short-term and long-term volatility have significant effects on future volatility predictions, and taking into account stock jumps, volatility and leverage effects will better characterize assets price dynamic process.