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Pricing model for path-dependent American options using tensors

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  • Kato, Kensuke

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.

Suggested Citation

  • Kato, Kensuke, 2026. "Pricing model for path-dependent American options using tensors," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 247(C), pages 175-209.
    • Handle: RePEc:eee:matcom:v:247:y:2026:i:c:p:175-209
    DOI: 10.1016/j.matcom.2026.03.013
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    References listed on IDEAS

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