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Multitouch Options

Author

Listed:
  • Tristan Guillaume

    (Laboratoire Thema, CYU Cergy Paris Université, 33 Boulevard du Port, F-95011 Cergy-Pontoise, Cedex, France)

Abstract

In this article, the multitouch option, also called the n - touch option (or the “baseball” option when n = 3 ) is analyzed and valued in closed form. This is a kind of barrier option that has been traded for a long time on the markets, but that does not yet admit a known valuation formula. The multitouch option sets a gradual knock-out/knock-in mechanism based on the number of times the underlying asset has crossed a predefined barrier in various time intervals before expiry. The higher the number of predefined time intervals during which the barrier has been touched, the lower the value of a knock-out contract at expiry, and conversely for a knock-in one. Multitouch options can be viewed as an extension of step barrier options, preserving the ability of the latter to adjust the exposure to risk over time, while eliminating the notorious danger of “sudden death” that holders of step barrier options are faced with. They are thus less risky and more flexible than step barrier options, and all the more so when compared to standard barrier options. This article also provides closed-form valuation of multitouch options with nonstandard features such as an outside barrier or a barrier defined as a continuous function of time.

Suggested Citation

  • Tristan Guillaume, 2023. "Multitouch Options," JRFM, MDPI, vol. 16(6), pages 1-29, June.
    • Handle: RePEc:gam:jjrfmx:v:16:y:2023:i:6:p:300-:d:1171110
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    References listed on IDEAS

    as
    1. M. Broadie & Y. Yamamoto, 2005. "A Double-Exponential Fast Gauss Transform Algorithm for Pricing Discrete Path-Dependent Options," Operations Research, INFORMS, vol. 53(5), pages 764-779, October.
    2. P. Carr, 1995. "Two extensions to barrier option valuation," Applied Mathematical Finance, Taylor & Francis Journals, vol. 2(3), pages 173-209.
    3. Grant Armstrong, 2001. "Valuation formulae for window barrier options," Applied Mathematical Finance, Taylor & Francis Journals, vol. 8(4), pages 197-208.
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