 Min–max multi-step barrier options and their variantsHangsuck Lee, Gaeun Lee and Seongjoo Song The North American Journal of Economics and Finance, 2023, vol. 67, issue C Abstract: This paper studies a new type of barrier option, min–max multi-step barrier options with diverse multiple up or down barrier levels placed in the sub-periods of the option’s lifetime. We develop the explicit pricing formula of this type of option under the Black–Scholes model and explore its applications and possible extensions. In particular, the min–max multi-step barrier option pricing formula can be used to approximate double barrier option prices and compute prices of complex barrier options such as discrete geometric Asian barrier options. As a practical example of directly applying the pricing formula, we introduce and evaluate a re-bouncing equity-linked security. The main theorem of this work is capable of handling the general payoff function, from which we obtain the pricing formulas of various min–max multi-step barrier options. The min–max multi-step reflection principle, the boundary-crossing probability of min–max multi-step barriers with icicles, is also derived. Keywords: Brownian motion; Reflection principle; Multi-step reflection principle; Esscher transform; Barrier option; Multi-step barrier; Icicles (search for similar items in EconPapers) Downloads: (external link) Related works: Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text Persistent link: https://EconPapers.repec.org/RePEc:eee:ecofin:v:67:y:2023:i:c:s1062940823000670 DOI: 10.1016/j.najef.2023.101944 Access Statistics for this article The North American Journal of Economics and Finance is currently edited by Hamid Beladi More articles in The North American Journal of Economics and Finance from Elsevier |
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