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Spanning Multi‐Asset Payoffs With ReLUs

Sébastien Bossu et al.

Mathematical Finance2025https://doi.org/10.1111/mafi.12454article
AJG 3ABDC A
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0.41

Abstract

We propose a distributional formulation of the spanning problem of a multi‐asset payoff by vanilla basket options. This problem is shown to have a unique solution if and only if the payoff function is even and absolutely homogeneous, and we establish a Fourier‐based formula to calculate the solution. Financial payoffs are typically piecewise linear, resulting in a solution that may be derived explicitly, yet may also be hard to exploit numerically. One‐hidden‐layer feedforward neural networks instead provide a natural and efficient numerical alternative for discrete spanning. We test this approach for a selection of archetypal payoffs and obtain better hedging results with vanilla basket options compared to industry‐favored approaches based on single‐asset vanilla hedges.

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https://doi.org/https://doi.org/10.1111/mafi.12454

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@article{sébastien2025,
  title        = {{Spanning Multi‐Asset Payoffs With ReLUs}},
  author       = {Sébastien Bossu et al.},
  journal      = {Mathematical Finance},
  year         = {2025},
  doi          = {https://doi.org/https://doi.org/10.1111/mafi.12454},
}

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Evidence weight

0.41

Balanced mode · F 0.40 / M 0.15 / V 0.05 / R 0.40

F · citation impact0.25 × 0.4 = 0.10
M · momentum0.55 × 0.15 = 0.08
V · venue signal0.50 × 0.05 = 0.03
R · text relevance †0.50 × 0.4 = 0.20

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