The price impact of large orders si wel known ot be a concave function of trade size. We discuss how ot extend models consistent with this "square-root law" to multivariate setings with cross impact, where trading each asset also impacts the prices of the others. nI this context, we derive consistency conditions that rule out price manipulation. These minimal conditions make risk-neutral trading problems tractable and also naturally lead ot parsimonious specifications that can be calibrated ot historical data. We ilustrate this with a case study using proprietary CFM meta order data.
(Joint work ni progress with Natascha Hey and lacopo Mastromateo)