Central limit theorems of range-based estimators for diffusion models

Abstract

In this article, we consider non parametric range-based estimation procedure for diffusion processes and propose a instantaneous volatility estimator. Under some weak conditions, we certify that the proposed estimator has convergence in probability. Adding some necessary conditions, we prove a central limit theorem. By inference, we reach a conclusion that, with high frequency data in hand, the proposed estimator is more precise than those pure realized instantaneous volatility ones. Numerical simulation illustrates the finite sample properties of the proposed estimator.

Keywords:

• Range-based instantaneous volatility estimator
• Central limit theorem
• Convergence in probability
• High frequency data

Acknowledgments

This work was jointly supported by the National Natural Science Foundation of China (61773217, 61374080, 11271189), the Natural Science Foundation of Jiangsu Province (BK20161552), Qing Lan Project of Jiangsu Province, the Philosophy and Social Science Foundation of Jiangsu Higher Education Institutions (2016SJB910002), Advanced Study and Training of Professional Leaders of Higher Vocational Colleges in Jiangsu (2017GRFX019).

Conflict of interest

The authors declare that there is no conflict of interest regarding the publication of this article.

Additional information

Funding

This work was jointly supported by the National Natural Science Foundation of China (61773217, 61374080, 11271189), the Natural Science Foundation of Jiangsu Province (BK20161552), Qing Lan Project of Jiangsu Province, the Philosophy and Social Science Foundation of Jiangsu Higher Education Institutions (2016SJB910002), Advanced Study and Training of Professional Leaders of Higher Vocational Colleges in Jiangsu (2017GRFX019).