Hidden Limit Orders and Liquidity in Limit Order Markets

Abstract

Many limit order markets allow limit order traders to submit orders (also called iceberg or undisclosed orders). Liquidity suppliers thus have possibility to post a quote and either display none or only a fraction of their order's quantity to market. Some recent empirical studies show that such orders represent a large proportion of market liquidity. These orders are indeed supposed to limit liquidity suppliers' risk of adverse selection and information disclosure. However, these orders could also be used by informed agents to trade a large volume without disseminating their private information. In this paper, we propose a theoretical sequential and discrete model of trading in a limit order book to investigate the impact of hidden orders on market performance and agents' welfare, when a limit order trader possesses a private information on realization of value of security with some probability. We show that submitting hidden orders may indeed be part of informed agent's equilibrium camouflage strategy. However, counter-intuitively, informed agent may be better off in transparent market. The move to an opaque market indeed increases total depth at best quotes in limit order book, but decreases visible depth. Thus it becomes more difficult, for informed agent, to get a large transaction volume in this market while replicating behavior of an uninformed limit order trader. We show that this effect can counterbalance what she earns by submitting hidden orders. Conversely, Bayesian and strategic uninformed market order trader beneficiates from a larger liquidity supply in opaque market.