# From Glosten-Milgrom to the whole limit order book and applications to financial regulation

## TL;DR

This paper develops an agent-based model of the limit order book incorporating different trader types, linking microstructure features to market dynamics, and providing tools for regulation and market analysis.

## Contribution

It extends the Glosten-Milgrom framework to model the entire limit order book and its relation to market microstructure and regulation applications.

## Key findings

- Model accurately predicts bid-ask spread and volume dynamics.
- Forecasts impact of tick size changes on market microstructure.
- Quantifies queue position value of limit orders.

## Abstract

We build an agent-based model for the order book with three types of market participants: informed trader, noise trader and competitive market makers. Using a Glosten-Milgrom like approach, we are able to deduce the whole limit order book (bid-ask spread and volume available at each price) from the interactions between the different agents. More precisely, we obtain a link between efficient price dynamic, proportion of trades due to the noise trader, traded volume, bid-ask spread and equilibrium limit order book state. With this model, we provide a relevant tool for regulators and market platforms. We show for example that it allows us to forecast consequences of a tick size change on the microstructure of an asset. It also enables us to value quantitatively the queue position of a limit order in the book.