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Multi-step barrier products and static hedging

Author

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  • Lee, Hangsuck
  • Choi, Yang Ho
  • Lee, Gaeun

Abstract

This paper examines multi-step barrier options with an arbitrary payoff function using extended static hedging methods. Although there have been studies using extended reflection principles to obtain joint distribution functions for barrier options with complex barrier conditions, and static hedging methods to evaluate limited barrier options with well-known payoff functions, we obtain an explicit expression of barrier option price which has a general payoff function under the Black–Scholes framework assumption. The explicit multi-step barrier options prices we discuss in this paper are not only useful in that they can handle different levels and time steps barrier and all types of payoff functions, but can also extend to pricing of barrier options under finite discrete jump–diffusion models with a simple barrier. In the last part, we supplement the theory with numerical examples of various multi-step barrier options under the Black–Scholes or discrete jump–diffusion model for comparison purposes.

Suggested Citation

  • 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).
    • Handle: RePEc:eee:ecofin:v:61:y:2022:i:c:s1062940822000316
    DOI: 10.1016/j.najef.2022.101676
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    References listed on IDEAS

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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. P Patel, Ravi & Nagababu, Garlapati & Kachhwaha, Surendra Singh & V V Arun Kumar, Surisetty & M, Seemanth, 2022. "Combined wind and wave resource assessment and energy extraction along the Indian coast," Renewable Energy, Elsevier, vol. 195(C), pages 931-945.
    3. 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).

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    More about this item

    Keywords

    Reflection principle; Multi-step reflection principle; Esscher transform; Barrier option; Multi-step barrier; Static hedging; Extended static hedging;
    All these keywords.

    JEL classification:

    • G13 - Financial Economics - - General Financial Markets - - - Contingent Pricing; Futures Pricing

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