An analysis of price impact function in order-driven markets

We introduce a microscopic model of double-auction markets based on random order placement. Traders post market or limit orders which are stored in the book of the exchange and executed via a central order matching mechanism. We use dimensional analysis, simulations and analytical approximations to make testable predictions of the price impact function. We find that the price impact function is always concave, in agreement with empirical measurements. We provide an explanation for its concavity based on the properties of order flows.