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Spanning Multi-Asset Payoffs With ReLUs

Author

Listed:
  • Sébastien Bossu

    (Department of Mathematics and Statistics [Charlotte] - UNC - University of North Carolina [Charlotte] - UNC - University of North Carolina System)

  • Stéphane Crépey

    (LPSM (UMR_8001) - Laboratoire de Probabilités, Statistique et Modélisation - SU - Sorbonne Université - CNRS - Centre National de la Recherche Scientifique - UPCité - Université Paris Cité, UPCité - Université Paris Cité)

  • Hoang-Dung Nguyen

    (LPSM (UMR_8001) - Laboratoire de Probabilités, Statistique et Modélisation - SU - Sorbonne Université - CNRS - Centre National de la Recherche Scientifique - UPCité - Université Paris Cité, UPCité - Université Paris Cité)

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

  • Sébastien Bossu & Stéphane Crépey & Hoang-Dung Nguyen, 2024. "Spanning Multi-Asset Payoffs With ReLUs," Working Papers hal-04505407, HAL.
    • Handle: RePEc:hal:wpaper:hal-04505407
    Note: View the original document on HAL open archive server: https://hal.science/hal-04505407v2
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