Information in Securities Markets: Kyle Meets Glosten and Milgrom

Kerry Back and Shmuel Baruch

Econometrica, 2004, vol. 72, issue 2, 433-465

Abstract: This paper analyzes models of securities markets with a single strategic informed trader and competitive market makers. In one version, uninformed trades arrive as a Brownian motion and market makers see only the order imbalance, as in Kyle (1985). In the other version, uninformed trades arrive as a Poisson process and market makers see individual trades. This is similar to the Glosten-Milgrom (1985) model, except that we allow the informed trader to optimize his times of trading. We show there is an equilibrium in the Glosten-Milgrom-type model in which the informed trader plays a mixed strategy (a point process with stochastic intensity). In this equilibrium, informed and uninformed trades arrive probabilistically, as Glosten and Milgrom assume. We study a sequence of such markets in which uninformed trades become smaller and arrive more frequently, approximating a Brownian motion. We show that the equilibria of the Glosten-Milgrom model converge to the equilibrium of the Kyle model. Copyright The Econometric Society 2004.

Date: 2004
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