Heavy-Tailed Features and Empirical Analysis of the Limit Order Book Volume Profiles in Futures Markets

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.