Robust pricing and hedging of double no-touch options

Abstract

Double no-touch options are contracts which pay out a fixed amount provided an underlying asset remains within a given interval. In this work, we establish model-independent bounds on the price of these options based on the prices of more liquidly traded options (call and digital call options). Key steps are the construction of super- and sub-hedging strategies to establish the bounds, and the use of Skorokhod embedding techniques to show the bounds are the best possible.

In addition to establishing rigorous bounds, we consider carefully what is meant by arbitrage in settings where there is no a priori known probability measure. We discuss two natural extensions of the notion of arbitrage, weak arbitrage and weak free lunch with vanishing risk, which are needed to establish equivalence between the lack of arbitrage and the existence of a market model.

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Correspondence to Jan Obłój.

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Cox, A.M.G., Obłój, J. Robust pricing and hedging of double no-touch options. Finance Stoch 15, 573–605 (2011). https://doi.org/10.1007/s00780-011-0154-z

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Keywords

  • Double no-touch option
  • Robust pricing and hedging
  • Skorokhod embedding problem
  • Weak arbitrage
  • Weak free lunch with vanishing risk
  • Model-independent arbitrage

Mathematics Subject Classification (2000)

  • 91B28
  • 60G40
  • 60G44

JEL Classification

  • C60
  • G13