Open Access
August 2020 Scaling limits for super-replication with transient price impact
Peter Bank, Yan Dolinsky
Bernoulli 26(3): 2176-2201 (August 2020). DOI: 10.3150/19-BEJ1189


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 (Math. Finance 22 (2012) 250–276) 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.


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Peter Bank. Yan Dolinsky. "Scaling limits for super-replication with transient price impact." Bernoulli 26 (3) 2176 - 2201, August 2020.


Received: 1 August 2019; Revised: 1 December 2019; Published: August 2020
First available in Project Euclid: 27 April 2020

zbMATH: 07193956
MathSciNet: MR4091105
Digital Object Identifier: 10.3150/19-BEJ1189

Keywords: binomial model , liquidity , Scaling limit , super-replication , transient price impact

Rights: Copyright © 2020 Bernoulli Society for Mathematical Statistics and Probability

Vol.26 • No. 3 • August 2020
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