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 scaling limit for ] temporary price impact . These models are a special case of our framework and so our probabilistic scaling limit argument allows one to expand the scope of the scaling limit result to path-dependent options .