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Valuation of exotic options under shortselling constraints


  • Uwe Wystup

    () (Commerzbank Treasury and Financial Products, Neue Mainzer Strasse 32-36, 60261 Frankfurtam Main, Germany Manuscript)

  • Uwe Schmock

    () (Department Mathematik, ETH Zentrum, CH-8092 Zürich, Switzerland)

  • Steven E. Shreve

    () (Department of Mathematical Sciences, Carnegie Mellon University, Pittsburgh, PA 15213, USA)


Options with discontinuous payoffs are generally traded above their theoretical Black-Scholes prices because of the hedging difficulties created by their large delta and gamma values. A theoretical method for pricing these options is to constrain the hedging portfolio and incorporate this constraint into the pricing by computing the smallest initial capital which permits super-replication of the option. We develop this idea for exotic options, in which case the pricing problem becomes one of stochastic control. Our motivating example is a call which knocks out in the money, and explicit formulas for this and other instruments are provided.

Suggested Citation

  • Uwe Wystup & Uwe Schmock & Steven E. Shreve, 2002. "Valuation of exotic options under shortselling constraints," Finance and Stochastics, Springer, vol. 6(2), pages 143-172.
  • Handle: RePEc:spr:finsto:v:6:y:2002:i:2:p:143-172
    Note: received: January 2000; final version received: February 2001

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    Cited by:

    1. Kasper Larsen & H. Mete Soner & Gordan Zitkovic, 2014. "Facelifting in Utility Maximization," Papers 1404.2227,
    2. Kasper Larsen & Halil Mete Soner & Gordan Žitković, 2016. "Facelifting in utility maximization," Finance and Stochastics, Springer, vol. 20(1), pages 99-121, January.
    3. Wurth, A.M., 2009. "Pricing and hedging in incomplete financial markets," Other publications TiSEM 45e60d16-cf9e-4740-bb05-0, Tilburg University, School of Economics and Management.
    4. repec:dau:papers:123456789/1930 is not listed on IDEAS
    5. Kasper Larsen & Halil Soner & Gordan Žitković, 2016. "Facelifting in utility maximization," Finance and Stochastics, Springer, vol. 20(1), pages 99-121, January.
    6. Chen, Yingshan & Dai, Min & Xu, Jing & Xu, Mingyu, 2015. "Superhedging under ratio constraint," Journal of Economic Dynamics and Control, Elsevier, vol. 58(C), pages 250-264.
    7. Imen Bentahar & Bruno Bouchard, 2006. "Barrier Option Hedging under Constraints: A Viscosity Approach," SFB 649 Discussion Papers SFB649DP2006-022, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.

    More about this item


    Exotic options; super-replication; stochastic control;

    JEL classification:

    • G13 - Financial Economics - - General Financial Markets - - - Contingent Pricing; Futures Pricing


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