Estimating spot volatility under infinite variation jumps with dependent market microstructure noise

TL;DR

This paper introduces a new estimator for spot volatility in high-frequency financial data that accounts for infinite variation jumps and dependent microstructure noise, achieving near-optimal efficiency.

Contribution

It proposes a novel hybrid estimator combining pre-averaging and empirical characteristic functions, with proven consistency, asymptotic normality, and near-efficient convergence rates.

Findings

Estimator is consistent and asymptotically normal.

Achieves near-efficient convergence rate under certain jump conditions.

Simulation studies confirm theoretical properties.

Abstract

Jumps and market microstructure noise are stylized features of high-frequency financial data. It is well known that they introduce bias in the estimation of volatility (including integrated and spot volatilities) of assets, and many methods have been proposed to deal with this problem. When the jumps are intensive with infinite variation, the efficient estimation of spot volatility under serially dependent noise is not available and is thus in need. For this purpose, we propose a novel estimator of spot volatility with a hybrid use of the pre-averaging technique and the empirical characteristic function. Under mild assumptions, the results of consistency and asymptotic normality of our estimator are established. Furthermore, we show that our estimator achieves an almost efficient convergence rate with optimal variance when the jumps are either less active or active with symmetric structure. Simulation studies verify our theoretical conclusions. We apply our proposed estimator to empirical analyses, such as estimating the weekly volatility curve using second-by-second transaction price data.