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Pricing Bounds on Barrier Options

Yukihiro Tsuzuki

Journal of Futures Markets, 2014, vol. 34, issue 12, 1170-1184

Abstract: This article proposes the optimal pricing bounds on barrier options in an environment where plain‐vanilla options and no‐touch options can be used as hedging instruments. Super‐ and sub‐hedging portfolios are derived without specifying any underlying processes, which are static ones consisting of not only plain‐vanilla options but also cash‐paying no‐touch options and/or asset paying no‐touch options that pay one cash or one underlying asset, respectively, if the barrier has not been hit. Moreover, the prices of these portfolios turn out to be the optimal pricing bounds through finding risk‐neutral measures under which the barrier option price is equal to the hedging portfolio's value. The model‐independent pricing bounds are useful because the price of a barrier option is significantly dependent on a model. It is demonstrated through numerical examples that prices outside the pricing bounds can be produced by models that are calibrated to market prices of plain‐vanilla options, but not to that of a no‐touch option. © 2013 Wiley Periodicals, Inc. Jrl Fut Mark 34:1170–1184, 2014

Date: 2014
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