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COS-TT-CHF: A Tensor-Train Characteristic-Function COS Method for Multi-Asset Option Pricing

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Listed:
  • Lucas Arenstein
  • Michael Kastoryano

Abstract

This paper considers European multi-asset option pricing under L\'evy and affine characteristic-function models. The main obstruction is the curse of dimensionality: direct multidimensional COS pricing forms tensor-product coefficient arrays whose size grows exponentially with the number of assets. We study and extend COS-TT-CHF, a low-rank construction that uses TT-cross to compress sampled characteristic-function tensors into tensor-train COS coefficients for arithmetic basket and min/max option pricing. Once built, the compressed representation gives fast post-setup strike-grid and selected component Delta/Vega calculations. The numerical study compares with adaptive-quadrature Fourier benchmarks, direct COS, a tensor-Fourier min-option benchmark, and quasi-Monte Carlo (QMC) references based on randomized Sobol points. The reported timings show a low-dimensional crossover against direct COS as the benchmark moves from $d=2$ to $d=4$, favorable timings against the tensor-Fourier min-option benchmark from $d=3$ onward, and favorable timings against the QMC common-Heston reference already at $d=2$. The reported tests reach $d=30$ for GBM and $d=20$ for VG, NIG, and common-Heston benchmark families, with accuracy, rank, runtime, control-sensitivity, and component Delta/Vega diagnostics reported throughout.

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  • Lucas Arenstein & Michael Kastoryano, 2026. "COS-TT-CHF: A Tensor-Train Characteristic-Function COS Method for Multi-Asset Option Pricing," Papers 2608.17636, arXiv.org.
    • Handle: RePEc:arx:papers:2608.17636
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    References listed on IDEAS

    as
    1. Fang, Fang & Oosterlee, Kees, 2008. "A Novel Pricing Method For European Options Based On Fourier-Cosine Series Expansions," MPRA Paper 9319, University Library of Munich, Germany.
    2. Lucas Arenstein & Michael Kastoryano, 2025. "Full grid solution for multi-asset options pricing with tensor networks," Papers 2601.00009, arXiv.org, revised Feb 2026.
    3. Rihito Sakurai & Koichi Miyamoto & Tsuyoshi Okubo, 2025. "Tensor train representations of Greeks for Fourier-based pricing of multi-asset options," Papers 2507.08482, arXiv.org.
    4. Michael Kastoryano & Nicola Pancotti, 2022. "A highly efficient tensor network algorithm for multi-asset Fourier options pricing," Papers 2203.02804, arXiv.org.
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