Dynamics of Order Positions and Related Queues in a Limit Order Book

TL;DR

This paper analyzes the limiting behavior and fluctuations of order positions and queues in a limit order book, providing explicit formulas for key quantities relevant to algorithmic trading.

Contribution

It introduces new fluid and diffusion limit results for order positions and queues, along with explicit analytical expressions in the context of limit order books.

Findings

Derived fluid and diffusion limits for order positions and queues

Provided explicit analytical expressions for key order book metrics

Analyzed fluctuations around fluid limits in limit order books

Abstract

Order positions are key variables in algorithmic trading. This paper studies the limiting behavior of order positions and related queues in a limit order book. In addition to the fluid and diffusion limits for the processes, fluctuations of order positions and related queues around their fluid limits are analyzed. As a corollary, explicit analytical expressions for various quantities of interests in a limit order book are derived.