A model of price impact and market maker latency

Price impact measures the difference between the best quoted price and the realized price as a function of order size. This paper analyzes how price impact depends on the latency that a market maker is subject to. I propose a tractable model which allows incorporating both order size and latency effects as determinants of price impact. The model is solved analytically and is novel in the theoretical microstructure literature. Larger latency increases adverse selection costs to the market maker and reduces his probability of trading with a slow investor. A larger order size decreases the slow trader's outside option, making him susceptible to accept a worse price for his trade. It is shown that the first-order effect of increased latency and increased order size is to increase price impact. Their joint impact is also positive. When the probability of trading is taken into consideration, the utility of the slow institutional investor decreases with increasing latency