Hidden Limit Orders and Liquidity in Limit Order Markets

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Abstract
Many limit order markets allow limit order traders to submit "hidden" orders (also called "iceberg" or "undisclosed" orders). Liquidity suppliers thus have the possibility to post a quote and either display none or only a fraction of their order's quantity to the market. Some recent empirical studies show that such orders represent a large proportion of the market liquidity. These orders are indeed supposed to limit the 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 the realization of the value of the security with some probability. We show that submitting hidden orders may indeed be part of the informed agent's equilibrium camouflage strategy. However, counter-intuitively, the informed agent may be better off in the transparent market. The move to an opaque market indeed increases the total depth at the best quotes in the limit order book, but decreases the visible depth. Thus it becomes more difficult, for the informed agent, to get a large transaction volume in this market while replicating the behavior of an uninformed limit order trader. We show that this effect can counterbalance what she earns by submitting hidden orders. Conversely, the Bayesian and strategic uninformed market order trader beneficiates from a larger liquidity supply in the opaque market.

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