Volatility Estimation and Forecasts Based on Price Durations

Abstract

We investigate price duration variance estimators that have long been neglected in the literature. In particular, we consider simple-to-construct non-parametric duration estimators, and parametric price duration estimators using autoregressive conditional duration specifications. This paper shows (i) how price duration estimators can be used for the estimation and forecasting of the integrated variance of an underlying semi-martingale price process and (ii) how they are affected by discrete and irregular spacing of observations, market microstructure noise, and finite price jumps. Specifically, we contribute to the literature by constructing the asymptotic theory for the non-parametric estimator with and without the presence of bid/ask spread and time discreteness. Further, we provide guidance about how our estimators can best be implemented in practice by appropriately selecting a threshold parameter that defines a price duration event, or by averaging over a range of non-parametric duration estimators. We also provide simulation and forecasting evidence that price duration estimators can extract relevant information from high-frequency data better and produce more accurate forecasts than competing realized volatility and option-implied variance estimators, when considered in isolation or as part of a forecasting combination setting.

High-Frequency Quote Volatility Measurement Using a Change-Point Intensity Model

“…Therefore, the measurement of instantaneous volatility lies in estimation of the intensity function associated with the process of δ−price changes, i.e., λ δ (t; F t ). A similar result is obtained in [4,5,17].…”

“…Cho and Frees [14] initiated a discussion of using price duration as volatility measurement, and Gerhard and Hautsch [15] formally proposed a volatility estimator based on price durations. Tse and Yang [16] developed duration-based variance estimators using ACD specifications, and recently, Hong et al [17] proposed a non-parametric duration-based estimator and concluded that the duration-based volatility estimators are more efficient than noise-robust realized volatility estimators. Furthermore, some papers focus on modeling the intensity function itself.…”

Forecasting stock return volatility: Realized volatility‐type or duration‐based estimators

“…where 1 6 ðδ=Y t N Þ 2 is the end-of-day bias correction. We follow Hong et al (2021) and implement the average of a range of NPDV estimators defined as follows:…”

“…Our baseline results, as well as this interesting empirical evidence, raise an obvious question: Theoretically, the durationbased estimators are designed to handle market microstructure noises and large jumps and avoid potential biases in the local volatility estimate. Hence, how can we rationalize their poorer empirical performance in China given the evidence in Andersen et al (2009) and Hong et al (2021) based on US data? Our second contribution is that we undertake a comprehensive set of simulation exercises to gain further insight into these estimators and explore, specifically, whether it is the occasional extreme level of volatility in the Chinese market that leads to the different forecasting performances.…”

“…The simulation exercises in Andersen et al (2009) and Hong et al (2021) set the annualized volatility to be 20% and 25%, respectively, which roughly match the average level of volatility in their sample. In our simulation exercises, we let the volatility of the stock diffusion process vary from 20% to 100% with intervals of 20% and fix the bid/ask spread at two ticks with trade durations to be 3 and 6 s, respectively.…”