Valuation of piecewise linear barrier options

Hangsuck Lee, Hongjun Ha and Minha Lee

The North American Journal of Economics and Finance, 2021, vol. 58, issue C

Abstract: This paper discusses the valuation of piecewise linear barrier options that generalize classical barrier options. We establish formulas for joint probabilities of the logarithmic returns of the underlying asset and its partial running maxima when the process has a piecewise constant drift. In particular, we show that our results embrace the famous reflection principle as a special case, and that our established proposition delivers useful scalability for computing desired probabilities related to various types of barriers. We derive the closed-form prices of piecewise linear barrier options under the Black–Scholes framework, which are obtainable with little effort by relying on the derived probabilities. In addition, we provide numerical examples and discuss how option prices respond to several types of piecewise linear barriers.

Keywords: Brownian motion; Piecewise linear barrier; Esscher transform; Refractive reflection principle; Barrier option (search for similar items in EconPapers)
JEL-codes: C65 G13 (search for similar items in EconPapers)
Date: 2021
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (5)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:ecofin:v:58:y:2021:i:c:s1062940821000929

DOI: 10.1016/j.najef.2021.101470

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