Applied Mathematics and Statistics Seminar by Sebastien Bossu: Spanning Multi-Asset Payoffs with ReLUs

Speaker: Sebastien Bossu, assistant professor of mathematics and statistics, University of North Carolina at Charlotte

 

Title: Spanning Multi-Asset Payoffs with ReLUs

 

Abstract: We propose a distributional formulation of the spanning problem of a multi-asset payoff by vanilla basket options. This problem has a unique solution if and only if the payoff is absolutely homogeneous, and we establish a Fourier-based formula to calculate it. Financial payoffs are typically piecewise linear, resulting in a solution that may be derived explicitly, yet may also be hard to exploit numerically. 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 than some industry-favored approaches. This presentation is based on joint work with Hoang-Dung Nguyen and Stéphane Crépey of Université Paris-Cité, published in Mathematical Finance, and includes an update on our recent results. An abridged version of the presentation will be given the following day at The Old Post Office as part of the CBOE Quant Conference 2026.

 

Bio: After 20 years of industry experience, Sébastien Bossu was appointed Assistant Professor of Mathematics and Statistics at UNC Charlotte. He has been principal at his startup investment and consulting company in New York City since 2011, and also served as part-time faculty at various institutions including NYU Courant and Johns Hopkins Carey Business School. Prior to moving to the U.S., Sébastien was a Director and Head of the Equity Derivatives Structuring team at Dresdner Kleinwort (now Commerzbank) in London, an Associate at J.P. Morgan in London, and a Jr. Trader at Goldman Sachs in Paris. He has written two textbooks on equity derivatives and several industry and academic articles. Sébastien received his Ph.D. in Quantitative Finance from Université Paris-Saclay under the guidance of Peter Carr, Stéphane Crépey and Andrew Papanicolaou, and he is also a graduate from The University of Chicago, HEC Paris, Columbia University and Sorbonne Université (fmr. Pierre-et-Marie-Curie).