No Tick-Size Too Small: A General Method for Modelling Small Tick Limit Order Books

Konark Jain (), Jean-François Muzy (), Jonathan Kochems and Emmanuel Bacry ()
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Konark Jain: UCL - University College of London [London]
Jean-François Muzy: SPE - Laboratoire « Sciences pour l’Environnement » (UMR CNRS 6134 SPE) - CNRS - Centre National de la Recherche Scientifique - Università di Corsica Pasquale Paoli [Université de Corse Pascal Paoli]
Jonathan Kochems: JP Morgan Chase London
Emmanuel Bacry: CEREMADE - CEntre de REcherches en MAthématiques de la DEcision - Université Paris Dauphine-PSL - PSL - Université Paris Sciences et Lettres - CNRS - Centre National de la Recherche Scientifique

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Abstract: Tick-sizes not only influence the granularity of the price formation process but also affect market agents' behavior. We investigate the disparity in the microstructural properties of the Limit Order Book (LOB) across a basket of assets with different relative tick-sizes. A key contribution of this study is the identification of several stylized facts, which are used to differentiate between large, medium, and small-tick assets, along with clear metrics for their measurement. We provide cross-asset visualizations to illustrate how these attributes vary with relative tick-size. Further, we propose a Hawkes Process model that {\color{black}not only fits well for large-tick assets, but also accounts for }sparsity, multi-tick level price moves, and the shape of the LOB in small-tick assets. Through simulation studies, we demonstrate the {\color{black} versatility} of the model and identify key variables that determine whether a simulated LOB resembles a large-tick or small-tick asset. Our tests show that stylized facts like sparsity, shape, and relative returns distribution can be smoothly transitioned from a large-tick to a small-tick asset using our model. We test this model's assumptions, showcase its challenges and propose questions for further directions in this area of research.

Keywords: Finance; Limit Order Book; Microstructure; Tick-Sizes; Simulation; Stylized Facts; Liquidity; Cross-Asset Visualization; Point Process; Trading and Market Microstructure (q-fin.TR); Computational Engineering; and Science (cs.CE); Computational Finance (q-fin.CP); FOS: Economics and business; FOS: Computer and information sciences; Hawkes Process (search for similar items in EconPapers)
Date: 2025-11-22
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