Approximate pricing of American exchange options with jumps

Guanghua Lian, Robert J. Elliott, Petko Kalev and Zhaojun Yang

Journal of Futures Markets, 2022, vol. 42, issue 6, 983-1001

Abstract: This paper presents a numerical method to price American exchange options based on jump‐diffusion processes. We first derive a closed‐form expression for the value of European exchange options, then decompose the value function of an American exchange option into a European counterpart, and an early exercise premium that is derived analytically. The early exercise boundary for an American exchange option approximately satisfies an algebraic equation that can be quickly numerically solved. Consequently, a formula is obtained for efficiently pricing American exchange options. The numerical results reveal that our pricing formula is robust and accurate.

Date: 2022
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https://doi.org/10.1002/fut.22316

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