title: Point process based high frequency volatility estimation
title: theory and applications
titleType: Subtitle
Creators: name: Li, Yifan
Publisher: name: Lancaster University
Year: 2018

description: 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.