Before revision:  We show that if the time step goes to zero and the effective resilience between consecutive trading timesremains constant then the limit of the super--replication prices coincide with the scaling limit for ]  temporary price impact with a modified market depth .
After revision:  We show that if the time step goes to zero and the effective resilience between consecutive trading timesremains constant then the limit of the super--replication prices coincide with the one obtained by PDE methods in ] temporary price impact with a modified market depth .