Valuing American options using multi-step rebate options

Hangsuck Lee, Hongjun Ha, Gaeun Lee and Minha Lee

The North American Journal of Economics and Finance, 2024, vol. 74, issue C

Abstract: The determination of optimal exercise boundaries is a critical aspect of pricing American options, which often requires costly numerical methods. This paper proposes a new approach that employs multi-step rebate options to approximate American option prices. Since the rebate options offer payoffs when the multi-step boundaries are touched, the prices of American options are estimated by maximizing the multi-step rebate option prices, and the optimal multi-step barriers replace the true optimal exercise boundaries. To this end, the closed-form pricing formulas for multi-step rebate options are derived and utilized to approximate several American option prices. Through extensive numerical experiments, we demonstrate the validity and performance of our approach.

Keywords: American option; American barrier option; American exchange option; Rebate option; First-hitting time (search for similar items in EconPapers)
JEL-codes: G13 (search for similar items in EconPapers)
Date: 2024
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Persistent link: https://EconPapers.repec.org/RePEc:eee:ecofin:v:74:y:2024:i:c:s1062940824001529

DOI: 10.1016/j.najef.2024.102227

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