A non-linear model of limit order book dynamics

TL;DR

This paper develops a non-linear dynamical system model for limit order book dynamics, transforming a Markov process into deterministic ODEs to analyze equilibrium distributions in market trading mechanisms.

Contribution

It introduces a novel approach by deriving a deterministic non-linear ODE model from a Markov process to study limit order book behavior.

Findings

Derivation of a deterministic dynamical system from a Markov process.

Approximate equilibrium distributions using fixed points of the ODEs.

Provides a framework for analyzing market trading mechanisms through non-linear models.

Abstract

This paper focuses on some simple models of limit order book dynamics which simulate market trading mechanisms. We start with a discrete time/space Markov process and then perform a re-scaling procedure leading to a deterministic dynamical system controlled by non-linear ODEs. This allows us to introduce approximants for the equilibrium distribution of the process represented by fixed points of deterministic dynamics.