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Spanning Multi-Asset Payoffs With ReLUs

Author

Listed:
  • S'ebastien Bossu

    (LPSM)

  • St'ephane Cr'epey

    (LPSM)

  • Hoang-Dung Nguyen

    (LPSM)

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 numerically exploit. 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.

Suggested Citation

  • S'ebastien Bossu & St'ephane Cr'epey & Hoang-Dung Nguyen, 2024. "Spanning Multi-Asset Payoffs With ReLUs," Papers 2403.14231, arXiv.org, revised Dec 2024.
    • Handle: RePEc:arx:papers:2403.14231
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    References listed on IDEAS

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    1. Zhenyu Cui & Yuewu Xu, 2022. "A new representation of the risk-neutral distribution and its applications," Quantitative Finance, Taylor & Francis Journals, vol. 22(5), pages 817-834, May.
    2. Terry Lyons & Sina Nejad & Imanol Perez Arribas, 2020. "Non-parametric Pricing and Hedging of Exotic Derivatives," Applied Mathematical Finance, Taylor & Francis Journals, vol. 27(6), pages 457-494, November.
    3. Henry Chiu & Rama Cont, 2023. "A model‐free approach to continuous‐time finance," Mathematical Finance, Wiley Blackwell, vol. 33(2), pages 257-273, April.
    4. Ilhan, Aytaç & Jonsson, Mattias & Sircar, Ronnie, 2009. "Optimal static-dynamic hedges for exotic options under convex risk measures," Stochastic Processes and their Applications, Elsevier, vol. 119(10), pages 3608-3632, October.
    5. Sébastien Bossu & Peter Carr & Andrew Papanicolaou, 2022. "Static replication of European standard dispersion options," Quantitative Finance, Taylor & Francis Journals, vol. 22(5), pages 799-811, May.
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