Jump-robust volatility estimation using dynamic dual-domain integration method

Abstract

In this paper, we propose a nonparametric procedure to estimate the volatility when the underlying price process is governed by Brownian semimartingale with jumps. The estimator combines the threshold technique and dynamic dual-domain integration approach for volatility when the price process is driven only by diffusions without jumps. The proposed estimator is consistent and asymptotically normal. A simulation study shows that the proposed estimator exhibits excellent performance over a wide range of jump sizes and for different finite sampling frequencies. A real data application is given to illustrate the potential applications of the proposed method.

Keywords:

• Volatility estimation
• dynamic integration
• time domain
• state domain
• short interest rate

MSC (2010):

• 60J60
• 91G70

JEL classification:

• C14
• C22
• E40

Acknowledgments

We are very grateful to an anonymous referee and the Editor for their valuable comments that have greatly improved the manuscript.

Additional information

Funding

This research was supported by the Guizhou Provincial Science and Technology Foundation (QianKeHeJichu [2019] No. 1286), Science and Technology Cooperation Plan Foundation of Guizhou Province of China (QianKeHeLHZi [2017] No. 7167), Key Project of Kaili University of China (Z1505), Cultivating Project of National Natural Science Foundation (QianKeHe talent-development platform [2017] No. 5723, QianKeHe talent-development platform [2017] No. 5723-02), the National Natural Science Foundation of China under Grant No. 11701286, and the Natural Science Foundation of Jiangsu Province of China under Grant No. BK20171073.