Multi-step barrier products and static hedging

Hangsuck Lee, Yang Ho Choi and Gaeun Lee

The North American Journal of Economics and Finance, 2022, vol. 61, issue C

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.

Keywords: Reflection principle; Multi-step reflection principle; Esscher transform; Barrier option; Multi-step barrier; Static hedging; Extended static hedging (search for similar items in EconPapers)
JEL-codes: G13 (search for similar items in EconPapers)
Date: 2022
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (3)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:ecofin:v:61:y:2022:i:c:s1062940822000316

DOI: 10.1016/j.najef.2022.101676

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