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  • 2018YifanLiPhd

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Point process based high frequency volatility estimation: theory and applications

Research output: ThesisDoctoral Thesis

Published
Publication date2018
Number of pages246
QualificationPhD
Awarding Institution
Supervisors/Advisors
Publisher
  • Lancaster University
Original languageEnglish

Abstract

This thesis is a compilation of three main studies with the common theme: point process based high-frequency volatility estimation. The first chapter introduces a new class of high-frequency volatility estimators and examines its asymptotic properties. The second chapter studies the relative importance of market microstructure (MMS) variables on high-frequency volatility estimation. The third chapter proposes a Markov-switching model for high-frequency volatility estimation and provides intraday measures of information contents in the trading process using the proposed model.
In the first chapter, we propose a novel class of volatility estimators named the Renewal Based Volatility (RBV) estimator, and derive its asymptotic properties. This class of estimators is motivated by the work of Engle and Russell (1998), Gerhard and Hautsch (2002), Andersen, Dobrev, and Schaumburg (2008), Tse and Yang (2012), Nolte, Taylor, and Zhao (2018), which use price durations to construct highfrequency volatility estimators. We show that our RBV estimator nests the volatility estimator using price duration, thus providing a theoretical framework to analyse its asymptotic properties. Our theoretical results support the simulation and empirical findings in Tse and Yang (2012) and Nolte, Taylor, and Zhao (2018) that: (1) both the non-parametric duration (NPD) based and the parametric duration (PD) based volatility estimators are more efficient than the Realized Volatility (RV) estimator; (2) a parametric design can greatly improve the efficiency of volatility estimation; (3) the PD estimator can provide accurate intraday volatility estimates. We provide simulation evidence for the performance of the NPD estimator and propose an exponentially smoothed version that can outperform noise-robust RV-type estimators under general market microstructure noise and jumps.
In the second chapter, we augment the PD estimator by including MMS variables in the parametric model. Specifically, we use a lognormal version of the Autoregressive Conditional Duration (ACD) model by Engle and Russell (1998), and include trading volume, bid-ask spread, total quote depth, quote depth difference, number of trades, order imbalance and order flow in the ACD model. Moreover, we use a best subset regression (BSR) approach to rank and select the included MMS variables. Our empirical study based on high-frequency trade and quote data from 29 highly liquid securities and a market index ETF shows that, by benchmarking on a Realized Kernel measure, the inclusion of MMS covariates significantly improves the performance of volatility estimates on both daily and intraday levels. The BSR approach is very effective in selecting the most relevant MMS covariates for volatility estimation, and it suggests that contemporaneous number of trades and order flow are the most important variables for intraday volatility estimation. More importantly, intraday volatility estimates can be constructed from the ACD model even in the case when the RV-type estimators cannot be reliably constructed due to a lack of data.
In the third chapter, we extend the Autoregressive Conditional Intensity (ACI) model (Russell, 1999) with a Markov-switching (MS) structure. We propose to use the Stochastic Approximation Expectation Maximization (SAEM) (Celeux and Diebolt, 1992) to estimate the MS-ACI model, and provide simulation evidence supporting the validity of the estimation procedure. We apply our MS-ACI model to high-frequency trade and quote data from 9 highly liquid securities and a market index ETF. Our empirical findings suggest that the MS-ACI model captures two distinct volume-volatility regimes in the high-frequency data: a dominant regime that spreads evenly throughout the trading day with strong correlation between cumulative trading volume and price duration, and a minor regime that concentrates at the beginning and end of a trading day with much weaker correlation between cumulative trading volume and price duration. We link this phenomenon to the firm-specific information arrival process into the market, and provide a measure of intraday information content of the transaction process.