Mathieu Rosenbaum - The two square root laws of market impact and their connection to rough volatility.

The goal of this work is to disentangle the roles of volume and participation rate in the price response of the market to a sequence of orders. To do so, we use an approach where price dynamics are derived from the order flow via no arbitrage constraints and make connections with the rough volatility paradigm. We also introduce in the model sophisticated market participants having superior abilities to analyse market dynamics. Our results lead to two square root laws of market impact, with respect to executed volume and with respect to participation rate. This is joint work with Bruno Durin and Grégoire Szymanski