  We prove a scaling limit theorem for the super-replication cost of options in
a Cox--Ross--Rubinstein binomial model with transient price impact. 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 one obtained by PDE methods in [12] for models with purely
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.
