Finance and Stochastics

, Volume 15, Issue 3, pp 573–605

Robust pricing and hedging of double no-touch options


DOI: 10.1007/s00780-011-0154-z

Cite this article as:
Cox, A.M.G. & Obłój, J. Finance Stoch (2011) 15: 573. doi:10.1007/s00780-011-0154-z


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.


Double no-touch optionRobust pricing and hedgingSkorokhod embedding problemWeak arbitrageWeak free lunch with vanishing riskModel-independent arbitrage

Mathematics Subject Classification (2000)


JEL Classification


Copyright information

© Springer-Verlag 2011

Authors and Affiliations

  1. 1.Department of Mathematical SciencesUniversity of BathBathUK
  2. 2.Mathematical Institute and Oxford-Man Institute of Quantitative FinanceUniversity of OxfordOxfordUK