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Valuation of exotic options under shortselling constraints

Author

Listed:
  • 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)

Abstract
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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    Citations

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    Cited by:

    1. Kasper Larsen & Halil Soner & Gordan Žitković, 2016. "Facelifting in utility maximization," Finance and Stochastics, Springer, vol. 20(1), pages 99-121, January.
    2. L.J. Basson & Sune Ferreira-Schenk & Zandri Dickason-Koekemoer, 2022. "Fractal Dimension Option Hedging Strategy Implementation During Turbulent Market Conditions in Developing and Developed Countries," International Journal of Economics and Financial Issues, Econjournals, vol. 12(2), pages 84-95, March.
    3. 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.
    4. Kasper Larsen & H. Mete Soner & Gordan Zitkovic, 2014. "Facelifting in Utility Maximization," Papers 1404.2227, arXiv.org.
    5. Bentahar, Imen & Bouchard, Bruno, 2006. "Barrier option hedging under constraints: A viscosity approach," SFB 649 Discussion Papers 2006-022, Humboldt University Berlin, Collaborative Research Center 649: Economic Risk.
    6. repec:dau:papers:123456789/1930 is not listed on IDEAS
    7. 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.
    8. repec:hum:wpaper:sfb649dp2006-022 is not listed on IDEAS
    9. Dylan Possamai & Nizar Touzi, 2020. "Is there a Golden Parachute in Sannikov's principal-agent problem?," Papers 2007.05529, arXiv.org, revised Oct 2022.

    More about this item

    Keywords

    Exotic options; super-replication; stochastic control;
    All these keywords.

    JEL classification:

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

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