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Pricing Bounds on Barrier Options
Author(s) -
Tsuzuki Yukihiro
Publication year - 2014
Publication title -
journal of futures markets
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.88
H-Index - 55
eISSN - 1096-9934
pISSN - 0270-7314
DOI - 10.1002/fut.21641
Subject(s) - exotic option , portfolio , valuation of options , cash , economics , barrier option , asset (computer security) , rational pricing , capital asset pricing model , financial economics , microeconomics , actuarial science , econometrics , computer science , finance , computer security
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