Research Markets

Glosten & Milgrom (1985) - Bid, Ask and Transaction Prices

Jan 1, 1985

Key Insights

The Glosten-Milgrom model explains the bid-ask spread as arising from adverse selection: market makers face a positive probability of trading against informed traders, so they set a spread compensating for the expected loss to informed order flow.

Market Microstructure Market Making Glosten-Milgrom (1985) Bid-Ask Model

Difficulty: Advanced Type: Research

Overview

Glosten and Milgrom (1985) develop a sequential trade model explaining the bid-ask spread as a consequence of adverse selection. Unlike inventory-based explanations, the model shows that even a risk-neutral market maker must set a positive spread when facing a positive probability of informed trading.

Model Framework

A specialist market maker posts bid and ask prices. Traders arrive sequentially — some informed (know true value), some uninformed (liquidity traders). The market maker updates beliefs about the asset's value using Bayes' rule after each trade, setting prices equal to expected value conditional on the next trade's direction.

The ask exceeds expected value because a buy order suggests informed traders believe the asset is undervalued; the bid is below expected value because a sell suggests overvaluation.

Key Results

Spread as adverse selection: The spread is proportional to the probability and magnitude of informed trading.
Bayesian learning: Prices are a martingale with respect to public information as market makers learn from order flow.
Spread dynamics: The spread narrows over time as more trades reveal information.
Market failure: If informed trading probability is too high, trade may break down entirely.

Significance

With Kyle (1985), the Glosten-Milgrom model is one of the two foundational pillars of market microstructure theory. It provides the theoretical basis for estimating adverse selection costs and analyzing market design, payment for order flow, and dark pool economics.