Volatility of Volatility: Estimation and Tests Based on Noisy High Frequency Data with Jumps

57 Pages Posted: 9 Mar 2021

See all articles by Yingying Li

Yingying Li

Hong Kong University of Science & Technology (HKUST), Dept of ISOM and Dept of Finance; Hong Kong University of Science & Technology (HKUST) - Department of Information Systems, Business Statistics and Operations Management; Hong Kong University of Science & Technology (HKUST) - Department of Finance

Guangying Liu

School of Statistics and Mathematics, Nanjing Audit University

Zhiyuan Zhang

Shanghai University of Finance and Economics - School of Statistics and Management

Date Written: February 11, 2021

Abstract

We establish a feasible central limit theorem with convergence rate $n^{1/8}$ for the estimation of the {integrated volatility of volatility} (VoV) based on noisy high-frequency data with jumps. This is the first inference theory ever built for VoV estimation under such a general setup. The central limit theorem is applied to provide interval estimates of the VoV and conduct hypothesis tests. Furthermore, when one is interested in the null hypothesis that the VoV is zero, we show that a more powerful test can be established based on a VoV estimator with a convergence rate $n^{1/5}$ under the null. Empirical results on the S\&P 500 and individual stocks show strong evidence of non-zero VoV.

Keywords: Volatility of Volatility, Central Limit Theorem, High Frequency Data, Microstructure Noise, Semimartingale

JEL Classification: C14, C22, G12

Suggested Citation

Li, Yingying and Liu, Guangying and Zhang, Zhiyuan, Volatility of Volatility: Estimation and Tests Based on Noisy High Frequency Data with Jumps (February 11, 2021). Journal of Econometrics, Forthcoming, Available at SSRN: https://ssrn.com/abstract=3783503

Yingying Li (Contact Author)

Hong Kong University of Science & Technology (HKUST), Dept of ISOM and Dept of Finance ( email )

Clear Water Bay, Kowloon
Hong Kong

Hong Kong University of Science & Technology (HKUST) - Department of Information Systems, Business Statistics and Operations Management ( email )

Clear Water Bay
Kowloon
Hong Kong

Hong Kong University of Science & Technology (HKUST) - Department of Finance ( email )

Clear Water Bay, Kowloon
Hong Kong

Guangying Liu

School of Statistics and Mathematics, Nanjing Audit University ( email )

No. 86 Yushan Western Road, Nanjing
Nanjing, Jiangsu 211815
China

Zhiyuan Zhang

Shanghai University of Finance and Economics - School of Statistics and Management ( email )

777 Guoding Road
Shanghai, Shanghai 200433
China

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