Volatility Decomposition and Estimation in Time-Changed Price Models

TL;DR

This paper investigates a volatility decomposition in time-changed price models, showing how separating tick-time volatility and trading intensity provides deeper insights and improves estimation accuracy, especially in the presence of microstructure noise.

Contribution

The paper introduces a novel approach to decompose and estimate volatility in time-changed models, enhancing understanding and estimation of market volatility.

Findings

Trading intensity significantly influences clock-time volatility fluctuations.

The proposed estimator has a better convergence rate due to microstructure noise mitigation.

Tick-time volatility curves are often smoother than clock-time volatility curves.

Abstract

The usage of a spot volatility estimate based on a volatility decomposition in a time-changed price-model according to the trading times is investigated. In this model clock-time volatility splits up into the product of tick-time volatility and trading intensity, which both can be estimated from data and contain valuable information. By inspecting these two curves individually we gain more insight into the cause and structure of volatility. Several examples are provided where the tick-time volatility curve is much smoother than the clock-time volatility curve meaning that the major part of fluctuations in clock-time volatility is due to fluctuations of the trading intensity. Since microstructure noise only influences the estimation of the (smooth) tick-time volatility curve, the findings lead to an improved pre-averaging estimator of spot volatility. This is reflected by a better rate of convergence of the estimator. The asymptotic properties of the estimators are derived by an infill asymptotic approach.