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Robust pricing and hedging of double no-touch options


Reference:

Cox, A. M. G. and Obłój, J., 2011. Robust pricing and hedging of double no-touch options. Finance and Stochastics, 15 (3), pp. 573-605.

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Official URL:

http://dx.doi.org/10.1007/s00780-011-0154-z

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.

Details

Item Type Articles
CreatorsCox, A. M. G.and Obłój, J.
DOI10.1007/s00780-011-0154-z
DepartmentsFaculty of Science > Mathematical Sciences
Publisher StatementRobust_Double_No_Touch_Author_Final.pdf: The original publication is available at www.springerlink.com
RefereedYes
StatusPublished
ID Code25612

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