From Glosten-Milgrom to the Whole Limit Order Book and Applications to Financial Regulation

26 Pages Posted: 21 Mar 2019

See all articles by Weibing Huang

Weibing Huang

Université Paris VI Pierre et Marie Curie - Laboratoire de Probabilités et Modèles Aléatoires (LPMA)

Mathieu Rosenbaum

Ecole Polytechnique, Palaiseau

Pamela Saliba

Ecole Polytechnique, Paris - Centre De Mathématiques Appliquées (CMAP); Autorité des Marchés Financiers

Date Written: February 27, 2019

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.

Keywords: market microstructure, limit order book, bid-ask spread, adverse selection, financial regulation, tick size, queue position valuation

Suggested Citation

Huang, Weibing and Rosenbaum, Mathieu and Saliba, Pamela and Saliba, Pamela, From Glosten-Milgrom to the Whole Limit Order Book and Applications to Financial Regulation (February 27, 2019). Available at SSRN: https://ssrn.com/abstract=3343779 or http://dx.doi.org/10.2139/ssrn.3343779

Weibing Huang

Université Paris VI Pierre et Marie Curie - Laboratoire de Probabilités et Modèles Aléatoires (LPMA) ( email )

Couloir 16-26, 1er étage
4, Place Jussieu
Paris, 75005
France

Mathieu Rosenbaum (Contact Author)

Ecole Polytechnique, Palaiseau ( email )

Route de Saclay
Palaiseau, 91128
France

Pamela Saliba

Autorité des Marchés Financiers ( email )

France

Ecole Polytechnique, Paris - Centre De Mathématiques Appliquées (CMAP) ( email )

France

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