We prove limit theorems for the super-replication cost of European options in a Binomial model with transient price impact. 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 .
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 .
R
limit theorems
a scaling limit theorem
D
European
R
Binomial
Cox--Ross--Rubinstein binomial
R
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
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
R
scaling limit for
one obtained by PDE methods in
A
12
A
for models with purely
R
with a modified market depth
. 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