Robust pricing and hedging of double no-touch options

Alexander M G Cox, Jan Obłój

Research output: Contribution to journalArticlepeer-review

64 Citations (SciVal)

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.

Original languageEnglish
Pages (from-to)573-605
Number of pages33
JournalFinance and Stochastics
Volume15
Issue number3
Early online date17 Mar 2011
DOIs
Publication statusPublished - 1 Sep 2011

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