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The pricing and static hedging of multi-step double barrier options

Author

Listed:
  • Lee, Hangsuck
  • Ko, Bangwon
  • Lee, Minha

Abstract

As a sequel to Lee et al. (2022b), this paper explores the pricing of multi-step double barrier options with arbitrary European-type payoffs from a static hedging perspective. Using the reflection principle of Brownian motion, we develop how to construct an exact static hedging portfolio consisting of simple discrete barrier options under the Black–Scholes model. This equivalent conversion from continuous monitoring to discrete ones provides an efficient way of evaluating multi-step double barrier options, while overcoming the drawbacks of dynamic hedging. We illustrate our result with numerical examples, and extend it to other asset price dynamics such as jump diffusion.

Suggested Citation

  • 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).
    • Handle: RePEc:eee:finlet:v:55:y:2023:i:pa:s1544612323002623
    DOI: 10.1016/j.frl.2023.103890
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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. Lee, Hangsuck & Jeong, Himchan & Lee, Minha, 2022. "Multi-step double barrier options," Finance Research Letters, Elsevier, vol. 47(PA).
    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. 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).
    5. Tristan Guillaume, 2010. "Step double barrier options," Post-Print hal-00924266, HAL.
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    8. Justin Lars Kirkby & Shijie Deng, 2019. "Static hedging and pricing of exotic options with payoff frames," Mathematical Finance, Wiley Blackwell, vol. 29(2), pages 612-658, April.
    9. 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).
    10. 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.
    11. Rolf Poulsen, 2006. "Barrier options and their static hedges: simple derivations and extensions," Quantitative Finance, Taylor & Francis Journals, vol. 6(4), pages 327-335.
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    More about this item

    Keywords

    Black–Scholes option price; Jump diffusion; Multi-step double barrier option; Static hedging;
    All these keywords.

    JEL classification:

    • G13 - Financial Economics - - General Financial Markets - - - Contingent Pricing; Futures Pricing
    • G22 - Financial Economics - - Financial Institutions and Services - - - Insurance; Insurance Companies; Actuarial Studies

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