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

ZHANG Chuanhai

Systems Engineering - Theory & Practice ›› 2019, Vol. 39 ›› Issue (4) : 946-969.

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Systems Engineering - Theory & Practice ›› 2019, Vol. 39 ›› Issue (4) : 946-969. DOI: 10.12011/1000-6788-2018-2059-24

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

  • ZHANG Chuanhai
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Abstract

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.

Key words

threshold pre-averaging modulated multipower / market microstructure noise / Lévy jumps / high-frequency data

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ZHANG Chuanhai. A new estimation for integrated volatility based on threshold pre-averaging modulated multi-power variation and its application. Systems Engineering - Theory & Practice, 2019, 39(4): 946-969 https://doi.org/10.12011/1000-6788-2018-2059-24

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Funding

Humanity and Social Science Youth Foundation of Chinese Ministry of Education (18YJC790210); The Fundamental Research Funds for the Central Universities, Zhongnan University of Economics and Law (2722019PY038)
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