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

ArXiv ID: 2410.08744 “View on arXiv”

Authors: Unknown

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: tick-size, limit order book, Hawkes Process, market microstructure, stylized facts, Equities

Complexity vs Empirical Score

  • Math Complexity: 8.5/10
  • Empirical Rigor: 6.0/10
  • Quadrant: Holy Grail
  • Why: The paper heavily employs advanced stochastic modeling (Hawkes processes, SPDEs, generator operators) with complex mathematical formulations, while also providing empirical analysis of stylized facts, cross-asset visualizations, and simulation studies to test model versatility.
  flowchart TD
    A["Research Goal<br>Modeling LOB dynamics across<br>different tick-size regimes"] --> B["Data Collection<br>Empirical LOB data from<br>equity markets with varying<br>relative tick-sizes"]
    B --> C["Methodology<br>Hawkes Process modeling<br>to capture event clustering"]
    C --> D{"Computational Analysis<br>Simulation & Parameter Estimation"}
    D --> E["Key Findings<br>Identified stylized facts<br>differentiating tick regimes"]
    E --> F["Outcomes<br>General model valid for both<br>large & small tick assets<br>Smooth transition between regimes"]