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

TL;DR

This paper introduces a comprehensive non-linear order book model derived from individual agent behaviors, providing new theoretical insights and formulas for market dynamics, and establishing a ranking method for market makers based on trading quality.

Contribution

It develops a general framework encompassing Markovian and Hawkes models, proving ergodicity and diffusivity, and deriving explicit formulas for key market quantities.

Findings

Proves ergodicity and diffusivity under mild conditions.

Provides closed-form formulas for market quantities.

Establishes a market maker ranking methodology.

Abstract

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.