Market impact as anticipation of the order flow imbalance

In this paper, we assume that the permanent market impact of metaorders is linear and that the price is a martingale. Those two hypotheses enable us to derive the evolution of the price from the dynamics of the flow of market orders. For example, if the market order flow is assumed to follow a nearly unstable Hawkes process, we retrieve the apparent long memory of the flow together with a power law impact function, which is consistent with the celebrated square root law. We also link the long memory exponent of the sign of market orders with the impact function exponent. One of the originalities of our approach is that our results are derived without assuming that market participants are able to detect the beginning of metaorders.