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Step double barrier options

Author

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  • Tristan Guillaume

    (THEMA - Théorie économique, modélisation et applications - UCP - Université de Cergy Pontoise - Université Paris-Seine - CNRS - Centre National de la Recherche Scientifique)

Abstract

Double barrier options have been traded for a long time in the markets and they are embedded in a variety of popular structured products. However, in their standard form, they lack flexibility inasmuch as they feature a constant barrier level during the entire option life. Step double barrier options overcome this limitation by allowing investors to set the knock-out or knock-in levels they want at the time of their choosing rather than by imposing an arbitrary mathematical form upon the time-varying double barrier. Although step double barrier options are actively traded, no analytical formula is known for their valuation and hedging. In this paper, not only regular step double barrier options are analytically valued, but also more exotic contracts combining periods with and without active barriers as well as step double barrier options written on several assets. Financial properties of these instruments are discussed in comparison with other existing contracts.

Suggested Citation

  • Tristan Guillaume, 2010. "Step double barrier options," Post-Print hal-00924266, HAL.
    • Handle: RePEc:hal:journl:hal-00924266
    Note: View the original document on HAL open archive server: https://hal.science/hal-00924266
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    Citations

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    Cited by:

    1. Lu, Yu-Ming & Lyuu, Yuh-Dauh, 2023. "Very fast algorithms for implied barriers and moving-barrier options pricing," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 205(C), pages 251-271.
    2. 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.
    3. Yuh‐Dauh Lyuu & Yu‐Quan Zhang, 2023. "Pricing multiasset time‐varying double‐barrier options with time‐dependent parameters," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 43(3), pages 404-434, March.
    4. 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.
    5. 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).
    6. Lee, Hangsuck & Lee, Gaeun & Song, Seongjoo, 2023. "Min–max multi-step barrier options and their variants," The North American Journal of Economics and Finance, Elsevier, vol. 67(C).
    7. Feng, Yun & Huang, Bing-hua & Young, Martin & Zhou, Qi-yuan, 2015. "Decomposing and valuing convertible bonds: A new method based on exotic options," Economic Modelling, Elsevier, vol. 47(C), pages 193-206.
    8. Fernández Lexuri & Hieber Peter & Scherer Matthias, 2013. "Double-barrier first-passage times of jump-diffusion processes," Monte Carlo Methods and Applications, De Gruyter, vol. 19(2), pages 107-141, July.
    9. 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.
    10. 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.
    11. Lee, Hangsuck & Jeong, Himchan & Lee, Minha, 2022. "Multi-step double barrier options," Finance Research Letters, Elsevier, vol. 47(PA).
    12. 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).
    13. Tristan Guillaume, 2019. "On the multidimensional Black–Scholes partial differential equation," Annals of Operations Research, Springer, vol. 281(1), pages 229-251, October.
    14. Hangsuck Lee & Gaeun Lee & Seongjoo Song, 2021. "Multi-step Reflection Principle and Barrier Options," Papers 2105.15008, arXiv.org.

    More about this item

    Keywords

    double barrier option; step barrier;

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