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:  The correct scaling turns out to keep the market depth parameter constant while resilience over fixed periods of time grows in inverse proportion with the duration between trading times. For vanilla options, the scaling limit is found to coincide with the scaling limit for ] temporary price impact with a modified market depth .