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In this paper, we assume that the permanent market impact of metaorders islinear and that the price is a martingale. Those two hypotheses enable us toderive the evolution of the price from the dynamics of the flow of marketorders. For example, if the market order flow is assumed to follow a nearlyunstable Hawkes process, we retrieve the apparent long memory of the flowtogether with a power law impact function which is consistent with thecelebrated square root law. We also link the long memory exponent of the signof market orders with the impact function exponent. One of the originalities ofour approach is that our results are derived without assuming that marketparticipants are able to detect the beginning of metaorders.

Market impact as anticipation of the order flow imbalance