Super-replication with nonlinear transaction costs and volatility uncertainty

TL;DR

This paper investigates super-replication of financial derivatives in illiquid markets with uncertain volatility, providing a dual characterization of super-replication prices and analyzing their behavior as trading frequency increases.

Contribution

It introduces a dual framework for super-replication under nonlinear costs and volatility bounds, extending existing models to include market illiquidity and uncertainty.

Findings

Dual representation of super-replication prices as supremum of penalized expectations

Scaling limit of super-replication prices as trading frequency increases

Extension of previous results to include nonlinear transaction costs and volatility uncertainty

Abstract

We study super-replication of contingent claims in an illiquid market with model uncertainty. Illiquidity is captured by nonlinear transaction costs in discrete time and model uncertainty arises as our only assumption on stock price returns is that they are in a range specified by fixed volatility bounds. We provide a dual characterization of super-replication prices as a supremum of penalized expectations for the contingent claim's payoff. We also describe the scaling limit of this dual representation when the number of trading periods increases to infinity. Hence, this paper complements the results in [11] and [19] for the case of model uncertainty.