Pricing model for path-dependent American options using tensors

Kensuke Kato

Mathematics and Computers in Simulation (MATCOM), 2026, vol. 247, issue C, 175-209

Abstract: This study proposes a pricing model for path-dependent American options with a single underlying asset. Generally, the price of derivatives including path dependency and American-style exercise cannot be calculated analytically. Moreover, its numerical calculation is complicated. Currently, a pricing framework does not exist for path-dependent American options. This study develops a comprehensive pricing model based on the binomial tree model which is suitable for valuing American options. We structure path dependent variables as one tensor quantity, adapting all paths on a binomial tree to tensor elements, and perform backward induction on each tensor element using the properties of the binomial lattice. Finally, we apply the model to representative path-dependent American options, including lookback, barrier, and Asian types, and analyze computational efficiency across different product characteristics.

Keywords: Path-dependent American option; Pricing model; Tensor representation; Binomial tree; Control variate method; Computational efficiency (search for similar items in EconPapers)
Date: 2026
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Persistent link: https://EconPapers.repec.org/RePEc:eee:matcom:v:247:y:2026:i:c:p:175-209

DOI: 10.1016/j.matcom.2026.03.013

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