A Limit Order Market with Uncertain Informed Trading Participation

Abstract

We study a one period limit order market with informed traders, noise traders, and competitive liquidity suppliers, in which the number of informed traders is random. Liquidity suppliers know the distribution of the informed trader count, but not its realization, and therefore face uncertainty about both the presence and the intensity of informed trading. We characterize equilibrium by a fixed point integral equation for the marginal cost function and establish existence of equilibrium for bounded asset values. We then analyse large order asymptotics. For bounded asset values with power law endpoint behaviour, equilibrium price impact follows a power law whose exponent is determined jointly by the asset value tail and the full distribution of the informed trader count. In particular, this exponent is not determined by the expected number of informed traders alone. In the light endpoint regime, price impact is instead logarithmic. Finally, we solve the fixed point numerically across several asset value and informed trader count distributions. The numerical results are consistent with the theoretical asymptotics in the cases covered by the theory and provide comparative statics beyond them.