Dynamical Trading Mechanism in Limit Order Markets

TL;DR

This paper models the microstructure of limit order markets as a dynamical system, analyzing the iterative trading process, stability, and controlled price dynamics to better understand market behavior.

Contribution

It introduces a dynamical trading mechanism model for limit order markets, combining combinatorial and stochastic analysis of trading processes and stability.

Findings

Analysis of stability conditions for the trading system

Insights into bid-ask pair dynamics and switching laws

Controlled spread and mid-price dynamics within small ranges

Abstract

This work's purpose is to understand the dynamics of limit order books in order-driven markets. We try to illustrate a dynamical trading mechanism attached to the microstructure of limit order markets. We capture the iterative nature of trading processes, which is critical in the dynamics of bid-ask pairs and the switching laws between different traders' types and their orders. In general, after introducing the atomic trading scheme, we study a general iterated trading process in both combinatorial and stochastic ways, and state a few results on the stability of a dynamical trading system. We also study the controlled dynamics of the spread and the mid-price in an iterated trading system, when their movements, generated from the dynamics of bid-ask pairs, are assumed to be restricted within some extremely small ranges.