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On Optimal Super-Hedging And Sub-Hedging Strategies

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  • YUKIHIRO TSUZUKI

    (Graduate School of Economics, University of Tokyo, 7-3-1, Hongo, Bunkyo-ku, Tokyo 113-0033, Japan)

Abstract

This paper proposes optimal super-hedging and sub-hedging strategies for a derivative on two underlying assets without any specification of the underlying processes. Moreover, the strategies are free from any model of the dependency between the underlying asset prices. We derive the optimal pricing bounds by finding a joint distribution under which the derivative price is equal to the hedging portfolio's value; the portfolio consists of liquid derivatives on each of the underlying assets. As examples, we obtain new super-hedging and sub-hedging strategies for several exotic options such as quanto options, exchange options, basket options, forward starting options, and knock-out options.

Suggested Citation

  • Yukihiro Tsuzuki, 2013. "On Optimal Super-Hedging And Sub-Hedging Strategies," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 16(06), pages 1-17.
    • Handle: RePEc:wsi:ijtafx:v:16:y:2013:i:06:n:s0219024913500386
    DOI: 10.1142/S0219024913500386
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    References listed on IDEAS

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    1. Michael Schmutz & Thomas Zurcher, 2010. "Static replications with traffic light options," Papers 1011.4795, arXiv.org.
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    Cited by:

    1. Alain Chateauneuf & Mina Mostoufi & David Vyncke, 2015. "Comonotonic Monte Carlo and its applications in option pricing and quantification of risk," Documents de travail du Centre d'Economie de la Sorbonne 15015, Université Panthéon-Sorbonne (Paris 1), Centre d'Economie de la Sorbonne.
    2. Akihiko Takahashi & Yukihiro Tsuzuki, 2017. "Rebalancing static super-replications," International Journal of Financial Engineering (IJFE), World Scientific Publishing Co. Pte. Ltd., vol. 4(01), pages 1-23, March.

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    2. Ilya Molchanov & Michael Schmutz, 2009. "Exchangeability type properties of asset prices," Papers 0901.4914, arXiv.org, revised Apr 2011.

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