Heavy-Tailed Features and Dependence in Limit Order Book Volume Profiles in Futures Markets

37 Pages Posted: 22 May 2013 Last revised: 5 May 2015

See all articles by Kylie-Anne Richards

Kylie-Anne Richards

University of Technology Sydney (UTS) - UTS Business School; University of New South Wales (UNSW) - School of Mathematics and Statistics; Macquarie University

Gareth Peters

Department of Actuarial Mathematics and Statistics, Heriot-Watt University; University College London - Department of Statistical Science; University of Oxford - Oxford-Man Institute of Quantitative Finance; London School of Economics & Political Science (LSE) - Systemic Risk Centre; University of New South Wales (UNSW) - Faculty of Science

William Dunsmuir

University of New South Wales

Date Written: March 17, 2015

Abstract

Extensive literature on the properties of the Limit Order Book (LOB) has emerged with the access to ultra-high frequency data from electronic exchanges. The study of fundamental statistical attributes in such data plays an increasingly important role in aspects of financial modelling. This research is of particular relevance to trading strategies and best execution practices to satisfy the increasing proliferation of regulation.

Only a limited number of studies have focused primarily on stochastic features of the volume process in the LOB, with the majority of studies centred on the price process. This paper investigates fundamental stochastic attributes of the random structures of the volume profiles in each level of the LOB. In particular, we investigate the ability to capture core features of the volume processes at different levels of depth under three families of models: alpha-stable, generalized Pareto distribution and generalized extreme value and find that there is statistical evidence that heavy-tailed sub-exponential volume profiles occur on the LOB bid and ask and on both intra-day and inter-day time scales. In futures exchanges, the heavy tail features are not asset class dependent and they occur on ultra or mid-range high frequency data. Of the distributions and estimation methods considered, the generalized Pareto distribution MLE provided the best fit for all assets. We demonstrate the impact of the appropriate modelling of the heavy tailed volume profiles on a commonly used liquidity measure, XLM. In addition, utilizing the generalized Pareto distribution to model LOB volume profiles allows one to avoid over-estimating the round trip cost of trading and also avoids erroneous estimations of volume leading to significant LOB imbalances in less liquid assets. We conclude that building blocks for any volume forecasting model should account for heavy tails, time varying parameters and long memory present in the data.

Keywords: Limit order book, Futures markets, High frequency volume profiles, Microstructure, Heavy tail

Suggested Citation

Richards, Kylie-Anne and Peters, Gareth and Dunsmuir, William, Heavy-Tailed Features and Dependence in Limit Order Book Volume Profiles in Futures Markets (March 17, 2015). Available at SSRN: https://ssrn.com/abstract=2268283 or http://dx.doi.org/10.2139/ssrn.2268283

Kylie-Anne Richards (Contact Author)

University of Technology Sydney (UTS) - UTS Business School ( email )

Sydney
Australia

University of New South Wales (UNSW) - School of Mathematics and Statistics ( email )

Sydney, 2052
Australia

Macquarie University ( email )

North Ryde
Sydney, New South Wales 2109
Australia

Gareth Peters

Department of Actuarial Mathematics and Statistics, Heriot-Watt University ( email )

Edinburgh Campus
Edinburgh, EH14 4AS
United Kingdom

HOME PAGE: http://garethpeters78.wixsite.com/garethwpeters

University College London - Department of Statistical Science ( email )

1-19 Torrington Place
London, WC1 7HB
United Kingdom

University of Oxford - Oxford-Man Institute of Quantitative Finance ( email )

University of Oxford Eagle House
Walton Well Road
Oxford, OX2 6ED
United Kingdom

London School of Economics & Political Science (LSE) - Systemic Risk Centre ( email )

Houghton St
London
United Kingdom

University of New South Wales (UNSW) - Faculty of Science ( email )

Australia

William Dunsmuir

University of New South Wales ( email )

Sydney, 2052
Australia

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