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American Options With Gradual Exercise Under Proportional Transaction Costs

Author

Listed:
  • ALET ROUX

    (Department of Mathematics, University of York, Heslington, York YO10 5DD, UK)

  • TOMASZ ZASTAWNIAK

    (Department of Mathematics, University of York, Heslington, York YO10 5DD, UK)

Abstract

American options in a multi-asset market model with proportional transaction costs are studied in the case when the holder of an option is able to exercise it gradually at a so-called mixed (randomized) stopping time. The introduction of gradual exercise leads to tighter bounds on the option price when compared to the case studied in the existing literature, where the standard assumption is that the option can only be exercised instantly at an ordinary stopping time. Algorithmic constructions for the bid and ask prices and the associated superhedging strategies and optimal mixed stopping times for an American option with gradual exercise are developed and implemented, and dual representations are established.

Suggested Citation

  • Alet Roux & Tomasz Zastawniak, 2014. "American Options With Gradual Exercise Under Proportional Transaction Costs," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 17(08), pages 1-36.
    • Handle: RePEc:wsi:ijtafx:v:17:y:2014:i:08:n:s0219024914500526
    DOI: 10.1142/S0219024914500526
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    Cited by:

    1. Alet Roux & Tomasz Zastawniak, 2016. "Game options with gradual exercise and cancellation under proportional transaction costs," Papers 1612.02312, arXiv.org.
    2. Johannes Gerer & Gregor Dorfleitner, 2018. "Optimal discrete hedging of American options using an integrated approach to options with complex embedded decisions," Review of Derivatives Research, Springer, vol. 21(2), pages 175-199, July.

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