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

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 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 stocks, 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 accounts for sparsity, multi-tick level price moves, and the shape of the book in small-tick stocks. Through simulation studies, we demonstrate the universality of the model and identify key variables that determine whether a simulated LOB resembles a large-tick or small-tick stock. 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.