Robust pricing and hedging of double no-touch options

Details Robust pricing and hedging of double no-touch options Robust pricing and hedging of double no-touch options

2009-01-06

arxiv.org/abs/0901.0674v1

Economy

Quantitative Finance

Pricing of Securities

32 pages, 5 figures

Scientific paper

Double no-touch options, contracts which pay out a fixed amount provided an underlying asset remains within a given interval, are commonly traded, particularly in FX markets. In this work, we establish model-free 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 {\it 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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