Agent-Based Order Books and Market Maker Quality Ranking

Summary

This document outlines a nonlinear order book model built from the behavior of individual market participants. Its framework includes both Markovian and Hawkes-based models, connecting agent-level order flow to aggregate market behavior. Under stated mild assumptions, the authors prove results concerning ergodicity and diffusivity, which describe long-run stability and price movement properties.

The model also yields closed-form expressions for quantities including the stationary distribution of best bid and ask sizes, the spread, liquidity fluctuations, and price volatility. These expressions are framed in terms of participants’ individual order flows. The authors then use the framework to propose a method for ranking market makers by trading quality. The supplied description does not specify the ranking criteria, assumptions in detail, empirical data, or comparative results, so it communicates the model’s scope and theoretical contributions without establishing how rankings perform in practice.

Key ideas

• The order book is modeled from the individual behavior of market participants.
• The framework encompasses Markovian and Hawkes-based order flow models.
• The authors prove ergodicity and diffusivity results under stated mild assumptions.
• Closed-form quantities link individual order flows to spread, liquidity, queue sizes, and volatility.
• The framework supports a proposed ranking of market makers by trading quality.

Tags

# From asymptotic properties of general point processes to the ranking of financial agents


# From asymptotic properties of general point processes to the ranking of financial agents









We propose a general non-linear order book model that is built from the individual behaviours of the agents. Our framework encompasses Markovian and Hawkes based models. Under mild assumptions, we prove original results on the ergodicity and diffusivity of such system. Then we provide closed form formulas for various quantities of interest: stationary distribution of the best bid and ask quantities, spread, liquidity fluctuations and price volatility. These formulas are expressed in terms of individual order flows of market participants. Our approach enables us to establish a ranking methodology for the market makers with respect to the quality of their trading.

Shown in full with attribution under the source's licence. Licence: abstract CC0

This summary was written by Stratmill's research agent from the original; it is not a copy of the source.