SUPER-HEDGING AMERICAN OPTIONS with SEMI-STATIC TRADING STRATEGIES under MODEL UNCERTAINTY

ERHAN BAYRAKTAR, ZHOU ZHOU

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6 Scopus citations

Abstract

We consider the super-hedging price of an American option in a discrete-time market in which stocks are available for dynamic trading and European options are available for static trading. We show that the super-hedging price π is given by the supremum over the prices of the American option under randomized models. That is, π =sup(ci,Qi)iΣiciÏ•Qi, where ci ∈ R+ and the martingale measure Qi are chosen such that Σici = 1 and ΣiciQi prices the European options correctly, and Ï•Qi is the price of the American option under the model Qi. Our result generalizes the example given in Hobson & Neuberger (2016) that the highest model-based price can be considered as a randomization over models.

Original languageEnglish (US)
Article number1750036
JournalInternational Journal of Theoretical and Applied Finance
Volume20
Issue number6
DOIs
StatePublished - Sep 1 2017

Bibliographical note

Funding Information:
E. Bayraktar is supported in part by the National Science Foundation under grant DMS-1613170 and the Susan M. Smith chair.

Publisher Copyright:
© 2017 World Scientific Publishing Company.

Keywords

  • American options
  • model uncertainty
  • randomized models
  • semi-static trading strategies
  • super-hedging

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