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Multi‐step reflection principle and barrier options

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  • Hangsuck Lee
  • Gaeun Lee
  • Seongjoo Song

Abstract

This paper examines a class of barrier options, multi‐step barrier options, which can have any finite number of barriers of any level. We obtain a general, explicit expression for option prices of this type under the Black–Scholes model by deriving the multi‐step reflection principle, that is, the multi‐step boundary‐crossing probability of Brownian motion. Multi‐step barrier options are not only useful in that they can handle barriers of different levels and time steps but can also approximate options with arbitrary barriers. Moreover, they can be applied to pricing barrier options under jump‐diffusion models.

Suggested Citation

  • Hangsuck Lee & Gaeun Lee & Seongjoo Song, 2022. "Multi‐step reflection principle and barrier options," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 42(4), pages 692-721, April.
    • Handle: RePEc:wly:jfutmk:v:42:y:2022:i:4:p:692-721
    DOI: 10.1002/fut.22306
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    References listed on IDEAS

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    1. Lee, Hangsuck & Ko, Bangwon & Song, Seongjoo, 2019. "Valuing step barrier options and their icicled variations," The North American Journal of Economics and Finance, Elsevier, vol. 49(C), pages 396-411.
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    Cited by:

    1. Lee, Hangsuck & Ko, Bangwon & Lee, Minha, 2023. "The pricing and static hedging of multi-step double barrier options," Finance Research Letters, Elsevier, vol. 55(PA).
    2. Lee, Hangsuck & Choi, Yang Ho & Lee, Gaeun, 2022. "Multi-step barrier products and static hedging," The North American Journal of Economics and Finance, Elsevier, vol. 61(C).
    3. Lee, Hangsuck & Jeong, Himchan & Lee, Minha, 2022. "Multi-step double barrier options," Finance Research Letters, Elsevier, vol. 47(PA).

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