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

TL;DR

This paper introduces a comprehensive method for modeling small tick limit order books, capturing their unique microstructural features and enabling smooth transition modeling between large and small tick assets.

Contribution

It develops a Hawkes Process model that accurately fits both large and small tick assets, accounting for sparsity, multi-tick moves, and order book shape, with cross-asset analysis and simulation validation.

Findings

Hawkes model fits well for large-tick assets

Model captures sparsity and shape differences

Smooth transition of stylized facts between asset types

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.