Exponential resilience and decay of market impact

Abstract

Assuming a particular price process, it was shown by Gatheral in [6], that a model that combines nonlinear price impact with exponential decay of market impact admits price manipulation, an undesirable feature that should lead to rejection of the model. Subsequently, Alfonsi and Schied proved in [2] that their model of the order book which has nonlinear market impact and exponential resilience, is free of price manipulation. In this paper, we show how these at-first-sight incompatible results are in reality perfectly compatible. © Springer-Verlag Italia 2011.