Authors: Giulia Iori, Polina Kovaleva and Maria Cristina Recchioni,
Status: Working Papers
Abstract: This paper studies optimal strategy of a liquidity-motivated trader in a public limit order book. We develop a continuous time diffusion framework which explains the trade-off between immediacy and a favorable transaction price. The key element in the model is a random delay parameter, which defers limit order execution and characterizes market liquidity. The probability density of the expected time-to-fill of limit orders sharpens as liquidity increases and reveals empirically ob- served exponential distribution of trading times. We obtain a closed-form solution that maximizes a risk averse trader’s utility function and demonstrate that the presence of the lag factor linearizes the impact of various other market parameters on the optimal limit price the trader submits. We also prove that, consistent with real market phenomena, the equilibrium bid-ask spread increases both as liquidity decreases and agents’ risk aversion increases.