Spanning Multi-Asset Payoffs With ReLUs

S\'ebastien Bossu, St\'ephane Cr\'epey and Hoang-Dung Nguyen
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S\'ebastien Bossu: LPSM
St\'ephane Cr\'epey: LPSM
Hoang-Dung Nguyen: LPSM

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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.

Date: 2024-03, Revised 2024-12
New Economics Papers: this item is included in nep-cmp
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