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On the Optimal Super- and Sub-Hedging Strategies

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  • Yukihiro Tsuzuki

    (Mizuho-DL Financial Technology Co., Ltd.
    The University of Tokyo)

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, 2012. "On the Optimal Super- and Sub-Hedging Strategies," CARF F-Series CARF-F-300, Center for Advanced Research in Finance, Faculty of Economics, The University of Tokyo, revised Aug 2013.
  • Handle: RePEc:cfi:fseres:cf300
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    File URL: http://www.carf.e.u-tokyo.ac.jp/pdf/workingpaper/fseries/312.pdf
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    References listed on IDEAS

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    1. Breeden, Douglas T & Litzenberger, Robert H, 1978. "Prices of State-contingent Claims Implicit in Option Prices," The Journal of Business, University of Chicago Press, vol. 51(4), pages 621-651, October.
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    3. Laurence, Peter & Wang, Tai-Ho, 2009. "Sharp distribution free lower bounds for spread options and the corresponding optimal subreplicating portfolios," Insurance: Mathematics and Economics, Elsevier, vol. 44(1), pages 35-47, February.
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    5. Chen, X. & Deelstra, G. & Dhaene, J. & Vanmaele, M., 2008. "Static super-replicating strategies for a class of exotic options," Insurance: Mathematics and Economics, Elsevier, vol. 42(3), pages 1067-1085, June.
    6. Umberto Cherubini & Elisa Luciano, 2002. "Multivariate Option Pricing with Copulas," ICER Working Papers - Applied Mathematics Series 05-2002, ICER - International Centre for Economic Research.
    7. Haydyn Brown & David Hobson & L. C. G. Rogers, 2001. "Robust Hedging of Barrier Options," Mathematical Finance, Wiley Blackwell, vol. 11(3), pages 285-314.
    8. David Hobson & Peter Laurence & Tai-Ho Wang, 2005. "Static-arbitrage upper bounds for the prices of basket options," Quantitative Finance, Taylor & Francis Journals, vol. 5(4), pages 329-342.
    9. David G. Hobson, 1998. "Robust hedging of the lookback option," Finance and Stochastics, Springer, vol. 2(4), pages 329-347.
    10. Margrabe, William, 1978. "The Value of an Option to Exchange One Asset for Another," Journal of Finance, American Finance Association, vol. 33(1), pages 177-186, March.
    11. Hobson, David & Laurence, Peter & Wang, Tai-Ho, 2005. "Static-arbitrage optimal subreplicating strategies for basket options," Insurance: Mathematics and Economics, Elsevier, vol. 37(3), pages 553-572, December.
    12. Jan Baldeaux & Marek Rutkowski, 2010. "Static Replication of Forward-Start Claims and Realized Variance Swaps," Applied Mathematical Finance, Taylor & Francis Journals, vol. 17(2), pages 99-131.
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    Cited by:

    1. repec:wsi:ijfexx:v:04:y:2017:i:01:n:s2424786317500037 is not listed on IDEAS
    2. 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 15015r, Université Panthéon-Sorbonne (Paris 1), Centre d'Economie de la Sorbonne, revised Jun 2015.
    3. 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.
    4. Alain Chateauneuf & Mina Mostoufi & David Vyncke, 2015. "Comonotonic Monte Carlo and its applications in option pricing and quantification of risk," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) hal-01159741, HAL.

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