Financial Engineering Workshop - Julien Guyon (Ecole des Ponts ParisTech)

Presenter: Julien Guyon (Ecole des Ponts ParisTech)

Presentation title
Neural Joint S&P 500/VIX Smile Calibration

Abstract
We calibrate neural stochastic differential equations jointly to S&P 500 smiles, VIX futures, and VIX smiles. Drifts and volatilities are modeled as neural networks. Minimizing a suitable loss allows us to fit market data for multiple S&P 500 and VIX maturities. A one-factor Markovian stochastic local volatility model is shown to fit both smiles and VIX futures within bid-ask spreads. The joint calibration actually makes it a pure path-dependent volatility model, confirming the findings in [Guyon, 2022, The VIX Future in Bergomi Models: Fast Approximation Formulas and Joint Calibration with S&P 500 Skew]. This is joint work with Scander Mustapha (Princeton).

Bio
Julien Guyon is a professor of Applied Mathematics at Ecole des Ponts ParisTech, one of the oldest and most prestigious French Grandes Ecoles, where he holds the BNP Paribas Chair Futures of Quantitative Finance, and an adjunct professor in the Departments of Mathematics at Columbia University (New York) and at Baruch College, City University of New York. Before joining Ecole des Ponts, Julien worked in the financial industry for 16 years, first in the Global Markets Quantitative Research team at Societe Generale in Paris (2006-2012), then as a senior quantitative analyst in the Quantitative Research group at Bloomberg L.P., New York (2012-2022). Julien was also an adjunct professor at the Courant Institute of Mathematical Sciences, NYU, from 2015 to 2022; and previously at Universite Paris Diderot and Ecole des Ponts ParisTech. Julien serves as an Associate Editor of Finance & Stochastics, SIAM Journal on Financial Mathematics,Quantitative Finance, and Journal of Dynamics and Games. He is also a Louis Bachelier Fellow.

Julien co-authored the book Nonlinear Option Pricing (Chapman & Hall, 2014) with Pierre Henry-Labordere. He has published more than 25 articles in peer-reviewed journals (including Finance and Stochastics, SIAM Journal on Financial Mathematics, Quantitative Finance, Risk, Journal of Computational Finance, Annals of Applied Probability, Stochastic Processes and their Applications) and is a regular speaker at international conferences, both academic and professional. His main research interests include volatility and correlation modeling, option pricing, optimal transport, and numerical probabilistic methods.

A big soccer fan, Julien has also published articles on fairness in sports both in academic journals and in top-tier newspapers including The New York Times, The Times, Le Monde, and El Pais. Some of his suggestions for draws and tournament design have been adopted by FIFA and UEFA, including a new, fairer draw method for the FIFA World Cup; a fairer format for the 2026 FIFA World Cup; a new knockout bracket for the UEFA Euro; and an optimized schedule of the UEFA Champions League. His paper "Risk of collusion: Will groups of 3 ruin the FIFA World Cup?" won the 2nd prize at the 2021 MIT Sloan Sports Analytics Conference, the biggest sports analytics event in the world.

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