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Multi-step double barrier options

Author

Listed:
  • Lee, Hangsuck
  • Jeong, Himchan
  • Lee, Minha

Abstract

In this article, we study double barrier options where the upper and lower boundaries are piecewise constant functions with arbitrary number of steps. We provide explicit formulas to price such types of options. On top of its applicability via generalized formulas, it is also shown that multi-step double barrier options can be applied to approximate the prices of options with arbitrary shapes of double barriers. Finally, numerical studies are provided to show validity and applicability of our theoretical findings in practice as well.

Suggested Citation

  • Lee, Hangsuck & Jeong, Himchan & Lee, Minha, 2022. "Multi-step double barrier options," Finance Research Letters, Elsevier, vol. 47(PA).
    • Handle: RePEc:eee:finlet:v:47:y:2022:i:pa:s1544612321005365
    DOI: 10.1016/j.frl.2021.102587
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    References listed on IDEAS

    as
    1. Choe, Geon Ho & Koo, Ki Hwan, 2014. "Probability of multiple crossings and pricing of double barrier options," The North American Journal of Economics and Finance, Elsevier, vol. 29(C), pages 156-184.
    2. Hélyette Geman & Marc Yor, 1996. "Pricing And Hedging Double‐Barrier Options: A Probabilistic Approach," Mathematical Finance, Wiley Blackwell, vol. 6(4), pages 365-378, October.
    3. 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.
    4. Xiao, Shuang & Ma, Shihua, 2016. "Pricing discrete double barrier options under Lévy processes: An extension of the method by Milev and Tagliani," Finance Research Letters, Elsevier, vol. 19(C), pages 67-74.
    5. Cho H. Hui, 1997. "Time‐dependent barrier option values," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 17(6), pages 667-688, September.
    6. Sheldon Lin, X., 1998. "Double barrier hitting time distributions with applications to exotic options," Insurance: Mathematics and Economics, Elsevier, vol. 23(1), pages 45-58, October.
    7. Tristan Guillaume, 2010. "Step double barrier options," Post-Print hal-00924266, HAL.
    8. Naoto Kunitomo & Masayuki Ikeda, 1992. "Pricing Options With Curved Boundaries1," Mathematical Finance, Wiley Blackwell, vol. 2(4), pages 275-298, October.
    9. Hangsuck Lee & Hongjun Ha & Minha Lee, 2022. "Piecewise linear double barrier options," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 42(1), pages 125-151, January.
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    Citations

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    Cited by:

    1. Lee, Hangsuck & Ha, Hongjun & Kong, Byungdoo, 2024. "Pricing first-touch digitals with a multi-step double boundary and American barrier options," Finance Research Letters, Elsevier, vol. 59(C).
    2. 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).
    3. Hangsuck Lee & Hongjun Ha & Gaeun Lee & Byungdoo Kong, 2025. "Two-Asset Double Barrier Options," Computational Economics, Springer;Society for Computational Economics, vol. 66(2), pages 1071-1106, August.
    4. Li, Xin, 2023. "Generalized two-barrier proportional step options," Finance Research Letters, Elsevier, vol. 51(C).
    5. Lee, Hangsuck & Lee, Minha & Song, Seongjoo, 2025. "Double-barrier lookback options," International Review of Financial Analysis, Elsevier, vol. 108(PA).
    6. Lee, Hangsuck & Lee, Minha & Ha, Hongjun, 2025. "Multi-piecewise linear double barrier options," Finance Research Letters, Elsevier, vol. 75(C).
    7. Lee, Hangsuck & Kye, Yisub & Kong, Byungdoo & Song, Seongjoo, 2025. "Multi-step double barrier options under time-varying interest rates," The North American Journal of Economics and Finance, Elsevier, vol. 76(C).
    8. Lee, Hangsuck & Ha, Hongjun & Kong, Byungdoo & Lee, Minha, 2023. "Pricing multi-step double barrier options by the efficient non-crossing probability," Finance Research Letters, Elsevier, vol. 54(C).

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    Keywords

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    JEL classification:

    • C65 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Miscellaneous Mathematical Tools
    • G13 - Financial Economics - - General Financial Markets - - - Contingent Pricing; Futures Pricing

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