  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).
