Valuing step barrier options and their icicled variations

Hangsuck Lee, Bangwon Ko and Seongjoo Song

The North American Journal of Economics and Finance, 2019, vol. 49, issue C, 396-411

Abstract: This paper intends to investigate an interesting class of barrier options, called step barrier options, whose barrier levels are a piecewise constant function of time. These options, while having transparent, simple, and flexible payoff structures, allow for explicit pricing formulas under the Black-Scholes model, and thus can be easily embedded into equity-linked products to enhance the yield or reduce the downside risk. Moreover, the class can be further generalized by attaching vertical branches of barriers to the horizontal one as in Lee and Ko (2018). Using the actuarial method of Esscher transform and the factorization formula, we derive the option pricing formulas under a more general framework with vertical branches attached to horizontal barriers. We explore the formulas through numerical examples, demonstrating their applicability to equity-linked investment with the step barrier option embedded.

Keywords: Black-Scholes model; Esscher transform; Step barrier option; Icicled barrier option; Reflection principle (search for similar items in EconPapers)
JEL-codes: G13 G22 (search for similar items in EconPapers)
Date: 2019
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (13)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:ecofin:v:49:y:2019:i:c:p:396-411

DOI: 10.1016/j.najef.2018.09.001

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