Asymptotic equivalence and sufficiency for volatility estimation under microstructure noise

TL;DR

This paper demonstrates that high-frequency financial data models with microstructure noise are asymptotically equivalent to Gaussian models, enabling the development of optimal volatility estimators.

Contribution

It establishes asymptotic equivalence between the complex microstructure noise model and a Gaussian shift model, facilitating simpler estimation methods.

Findings

Asymptotic equivalence to Gaussian shift model proven

Constructed rate-optimal volatility estimators

Developed efficient integrated volatility estimators

Abstract

The basic model for high-frequency data in finance is considered, where an efficient price process is observed under microstructure noise. It is shown that this nonparametric model is in Le Cam's sense asymptotically equivalent to a Gaussian shift experiment in terms of the square root of the volatility function $\sigma$. As an application, simple rate-optimal estimators of the volatility and efficient estimators of the integrated volatility are constructed.