Permanent market impact can be nonlinear
There are two schools of thought regarding market impact modeling. On the one hand, seminal papers by Almgren and Chriss introduced a decomposition between a permanent market impact and a temporary (or instantaneous) market impact. This decomposition is used by most practitioners in execution models. On the other hand, recent research advocates for the use of a new modeling framework that goes down to the resilient dynamics of order books: transient market impact. One of the main criticisms against permanent market impact is that it has to be linear to avoid dynamic arbitrage. This important discovery made by Huberman and Stanzl and Gatheral favors the transient market impact framework, as linear permanent market impact is at odds with reality. In this paper, we reconsider the point made by Gatheral using a simple model for market impact and show that permanent market impact can be nonlinear. Also, and this is the most important part from a practical point of view, we propose different statistics to estimate permanent market impact and execution costs that generalize the ones proposed in Almgren at al. (2005).