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arXiv · 2403.14231

Spanning Multi-Asset Payoffs With ReLUs

Sébastien Bossu·Stéphane Crépey·Hoang-Dung Nguyen
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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.

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Sébastien Bossu, Stéphane Crépey, Hoang-Dung Nguyen. 2024-03-21. Spanning Multi-Asset Payoffs With ReLUs. https://arxiv.org/abs/2403.14231

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