Spanning Multi-Asset Payoffs With ReLUs

Sébastien Bossu (), Stéphane Crépey () and Hoang-Dung Nguyen ()
Additional contact information
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

Working Papers from HAL

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.

Keywords: Carr-Madan spanning formula; basket options; Fourier transform; iterated integrals; measures; distributions; Cauchy principal value integral; one-hidden-layer feedforward ReLU neural network; dispersion call; static hedging; 62G08; 62M45; 42B10; 46A11; 91G20 (search for similar items in EconPapers)
Date: 2024-11-29
Note: View the original document on HAL open archive server: https://hal.science/hal-04505407v5
References: Add references at CitEc
Citations:

Downloads: (external link)
https://hal.science/hal-04505407v5/document (application/pdf)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:hal:wpaper:hal-04505407

Access Statistics for this paper

More papers in Working Papers from HAL
Bibliographic data for series maintained by CCSD ().