基于门限预平均已调整多次幂变差的可积波动估计及其应用

本文在市场微观结构噪声和跳跃下新提出一类可积波动估计.这些估计联合采用了预平均已调整多次幂变差估计和门限技术,分别消除噪声和跳跃的影响.我们同时给出这一估计的渐近性质,包括一致性和中心极限定理.蒙特卡罗模拟结果表明这一估计对噪声和Lévy跳跃稳健,并且相比预平均已调整多次幂变差(PMMV)估计(Vetter, 2008)具有更好的表现.在实证应用中,基于中国股市逐笔交易的高频数据估计出2015年股灾前后上证50成分股的连续波动,跳跃波动以及噪声波动,并且研究了它们之间相互关系.实证发现:1)噪声波动对潜在收益波动具有正向预测作用,但该预测作用主要针对连续波动,对跳跃波动预测作用并不显著;2)噪声波动具有很强的相依性,连续波动对其具有显著正向预测作用,而跳跃波动对其不存在显著的预测能力.本文研究结果表明噪声包含了有助于潜在价格波动预测的信息,不完全是"噪声",其包含的信息有待深入挖掘.

A new estimation for integrated volatility based on threshold pre-averaging modulated multi-power variation and its application

This paper develops a new class of estimators for integrated volatility in the presence of market microstructure noise and jumps. These estimators are based on the simultaneous use of pre-averaged modulated multi-power variation estimation and the threshold technique, which serve to remove microstructure noise and jumps respectively. We also prove the asymptotic properties of the proposed estimators, including consistency and the associated central limit theorems. Monte Carlo simulations show that these estimators are robust to both microstructure noise and Lévy jumps and provide better performances than pre-averaged modulated multi-power variation (PMMV) estimation (Vetter, 2008). In the empirical applications, using the tick by tick high-frequency data from the Chinese stock market, we estimate continuous volatility, jump volatility and noise variance for SSE 50 component stocks during the stock market crash in 2015 based on our new estimators, and study the relationships among them. The main findings are summarized as follows:1) noise volatility has significantly positive predictability for total volatility of underlying returns, however, such predictability holds mainly for continuous volatility rather than jump volatility; 2) continuous volatility, rather than jump volatility, has significantly positive predictability for noise volatility that exhibits strong dependence. The results imply that noise is not pure "noise", instead, it contains some useful information that helps predict volatility of the underlying asset price and such information merits further research.