A Formal Dynamic Model of Market Making

Abstract

In a recent issue of this journal Barnea [1] presented an empirical study of the impact of a specialist (market-maker) on the variability of the price of a stock. He concludes with others that “the chief cost of dealing with a market maker is the difference between the theoretical but unobservable equilibrium price and the transaction price, rather than the bid-ask spread.” This paper presents a rigorous dynamic model in which the specialist, who is uncertain about the future arrival of tenders, determines transaction prices periodically over the trading day. The structure of the model permits a direct comparison of the specialist's prices to the “equilibrium price,” to be defined below, and also to what prices would be in the absence of a specialist.