Pricing first-touch digitals with a multi-step double boundary and American barrier options

Hangsuck Lee, Hongjun Ha and Byungdoo Kong

Finance Research Letters, 2024, vol. 59, issue C

Abstract: A first-touch digital option delivers a payoff when an underlying variable first touches a given boundary, and most studies discuss its pricing by assuming a single flat boundary and a fixed payout amount. This paper derives explicit pricing formulas for first-touch digital options with a multi-step double boundary and customizable payoffs. To this end, we establish the probabilities of the first-hitting times of a Brownian motion for the multi-step double boundary. Furthermore, we explain how the first-touch digital option pricing formulas approximate an American knock-out multi-step barrier option.

Keywords: First-hitting time; Multi-step double boundary; Digital option; American barrier option (search for similar items in EconPapers)
JEL-codes: G13 G22 (search for similar items in EconPapers)
Date: 2024
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:finlet:v:59:y:2024:i:c:s1544612323010711

DOI: 10.1016/j.frl.2023.104699

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