Bid, Ask and Transaction Prices in a Specialist Market with Heterogeneously Informed Trades Lawrence Glosten Paul Milgrom

Overview Specialist faces an adverse selection problem. (A customer knows something the specialist does not.) The Basic Model  Using a formal model to show how the spread arises from adverse selection.  Examination some of the dynamic properties of the spread and transaction prices. Five Propositions Conclusion

The Basic Model

Investor’s optimal decision

Specialist’s Expected Profits

Propositions 1.Bid and ask prices straddle the price that would prevail if all traders had the same information as the specialist. 2. Prices at which transactions actually occur form a martingale. 3.A bound on the size of the spread that can arise from adverse selection. 4.The value expectations of the specialist and the insiders tend to converge. 5.How the spread responds to variations in the parameters of the model

Proposition 1

Proposition 2

Proposition 3

Proposition 4

Proposition 5

Conclusion Adverse selection can account for the existence of a spread between the ask and bid prices. The average magnitude of the spread depends on the exogenous arrival patterns of insiders and liquidity readers, the elasticity of supply and demand among liquidity traders, and the quality of the information held by insiders. Transaction prices are informative and hence spreads tend to decline with trade.