Super-replication with nonlinear transaction costs and volatility uncertainty

Peter Bank, Yan Dolinsky, Selim Gökay

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8 Citations (Scopus)

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 [Finance Stoch. 17 (2013) 447-475] and [Ann. Appl. Probab. 5 (1995) 198-221] for the case of model uncertainty.

Original languageEnglish
Pages (from-to)1698-1726
Number of pages29
JournalAnnals of Applied Probability
Volume26
Issue number3
DOIs
Publication statusPublished - 1 Jun 2016
Externally publishedYes

Keywords

  • Hedging with friction
  • Limit theorems
  • Super-replication
  • Volatility uncertainty

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