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

2024-10-11

arXiv.org

AI Summary

This study systematically investigates the impact of relative tick size on limit order book (LOB) microstructure, aiming to identify and quantify distinct characteristics across assets with large, medium, and small tick sizes. We propose the first multidimensional Hawkes process model capable of smoothly capturing cross-tick-size LOB dynamics—unifying the modeling of order sparsity, multi-level price jumps, and bid-ask spread shape. We introduce the first formal microstructural criterion for classifying small-tick stocks. Furthermore, we uncover a universal mapping between tick size and order flow dynamics. The model is validated against empirical stylized facts, successfully reproducing key small-tick LOB features—including sparsity, spread shape, and heavy-tailed, leptokurtic return distributions—and enables continuous parameter-driven simulation of LOB evolution from large- to small-tick regimes, demonstrating its cross-asset generalizability.

Technology Category

• Cognitive Modeling & Cognitive Systems: Neural Spike Coding
• Natural Language Processing: (Large) Language Models
• Machine Learning: Large Multimodal Models (LMMs)

Application Category

• Web Mining and Content Analysis: Models for Web evolution
• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Security and Privacy: Large-scale security measurements

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.

Problem

• Modeling Limit Order Books for varying tick-sizes
• Differentiating microstructural properties across asset types
• Developing a versatile Hawkes Process model for LOBs

Innovation

• Hawkes Process model for diverse tick-sizes
• Cross-asset visualization of tick-size effects
• Metrics differentiating large and small-tick assets