NEWS

- The French sports daily L'Équipe has published an article on my work to build a fair ranking of the league phase of the new UEFA Champions League. The new format (a league phase where all 36 teams are ranked in a unique table, but each team only plays against 8 opponents) raises the important question: "What is a fair ranking?". We use various statistical (Poisson) models on goals scored to answer those questions. This is joint work with my students at École nationale des ponts et chaussées.

- I was live on La chaîne L'Équipe in the TV program L'Équipe du soir on Jan 20, 2025 (from 33 min 20 sec) and on Jan 22, 2025 (from 14 min) to discuss the probabilities that teams advance to the next round of the UEFA Champions League, as well as a mathematical indicator that I have devised to measure the importance of a game.

- This work was also featured in two articles in L'Équipe (here and here) and in two articles in Le Télégramme (here and here).

- I was voted Risk's 2025 Quant of the Year. I am truly honored. It is a great feeling to see my work on path-dependent volatility and on the joint calibration of S&P 500 and VIX smiles recognized by such a major award.
This achievement would not have been possible without my co-authors and collaborators, whom I warmly thank, with a special thank you to Scander Mustapha and Florian Bourgey, my co-authors on the awarded papers.

- I was live on La chaîne L'Équipe in the TV program L'Équipe du soir (from 11 min 45 sec) on August 29, 2024 to discuss the new format of the UEFA Champions League.

- New paper is out! Pricing and Calibration in the 4-Factor Path-Dependent Volatility Model. This is joint work with Guido Gazzani.

- Spring 2024: I am proud to teach the joint chair lecture "Advanced calibration methods and VIX derivatives" of the BNP Paribas chair Futures of Quantitative Finance at Université Paris Cité. This is the first joint Masters course of the famous math finance programs run by Sorbonne Université, Université Paris Cité, and École des Ponts ParisTech.

- February 2024: Our new paper "Fast Exact Joint S&P 500/VIX Smile Calibration in Discrete and Continuous Time" is published in Risk (joint work with Florian Bourgey).

- I was live on La chaîne L'Équipe for 2.5 hours during the draws of the round of 16 of the 2023-24 UEFA Champions League, as well as the draws of the knockout playoffs of the Europa League and Europa Conference League, showing how the draw probabilities evolved live during the draws and commenting on them. See the free YouTube link.

- Together with my students Flavien Audibert, Bilel Benaich, Yohann Canavese, and Akram Lamssyah, we have created a live probability calculator that computes the exact draw probabilities as they evolve during the draws of the round of 16 of the UEFA Champions League and the knockout playoffs of the Europa League and Europa Conference League. Due to the draw constraints and draw procedure, the probabilities are not easy at all to compute! The graph theory method that we used is explained here.

- See also my article Un PSG-Bayern Munich en huitièmes de finale de la Ligue des champions ? Probable, mais... in Le Monde, December 18, 2023 (in French).

- December 2023: Our paper "Neural Joint S&P 500/VIX Smile Calibration" is published in Risk (joint work with Scander Mustapha).

- Fall 2023: I am very happy to join the faculty at the Department of Mathematics at Baruch College, City University of New York, where I teach the course "Advanced Computational Methods in Finance" in the Master of Financial Engineering.

- Fall 2023: I am very happy to carry on teaching in the Department of Mathematics at Columbia University, where I teach the course "Nonlinear Option Pricing" in the MAFN program.

- Ingenius, the digital review of Ecole des Ponts ParisTech, published my article Using mathematics for a fairer FIFA World Cup in their October 2023 issue.

- August 2023: Our paper Does the Term-Structure of the At-the-Money Skew Really Follow a Power Law? (joint work with Mehdi El Amrani) has been published in Risk. It is available online here, and the preprint is available here.

- August 2023: Our article Volatility Is (Mostly) Path-Dependent (joint work with Jordan Lekeufack) has been published in Quantitative Finance. The preprint is available here.

- Fall 2022: I'll be presenting our recent paper "Volatility Is (Mostly) Path-Dependent" at the Bachelier seminar (Paris) on Sep 30, at the Stochastic Methods in Finance seminar (Ecole des Ponts) on Oct 3, at the 18th Quantitative Finance conference in Dubrovnik on Oct 20, at the ETH Zurich seminar on Insurance Mathematics and Stochastic Finance on Oct 27, and at QuantMinds 2022 in Barcelona on Nov 8.

- I'm proud to join École des Ponts ParisTech, one of the top engineering schools in France, as a full professor of -- and researcher in -- Applied Mathematics, starting September 1, 2022. So, quite a big change, moving full time to academia and moving back to Paris, after 10 fantastic years at Bloomberg LP in New York. I'm looking forward to this new academic life ahead -- academic but still very connected with the industry in many ways, I hope, as I have always loved bridging both worlds!

- July 2022: our new article "Volatility Is (Mostly) Path-Dependent" is finally out! And we believe it is an important contribution to volatility modeling. Indeed, we learn from data that volatility is mostly path-dependent: at least 85-90% of the variance of the implied volatility of equity indexes is explained endogenously by past index returns, and around 60% for (noisy estimates of) future daily realized volatility. The path-dependency that we uncover is remarkably simple: a linear combination of a weighted sum of past daily returns and the square root of a weighted sum of past daily squared returns with different time-shifted power-law weights capturing both short and long memory. This simple model, which is homogeneous in volatility, is shown to consistently outperform existing models across equity indexes for both implied and realized volatility. It suggests a simple continuous-time path-dependent volatility (PDV) model that may be fed historical or risk-neutral parameters. The weights can be approximated by superpositions of exponential kernels to produce Markovian models. In particular, we propose a 4-factor Markovian PDV model which captures all the important stylized facts of volatility, produces very realistic price and volatility paths, and jointly fits SPX and VIX smiles remarkably well. We thus show, for the first time, that a continuous-time Markovian parametric stochastic volatility (actually, PDV) model can practically solve the joint SPX/VIX smile calibration problem. This article is dedicated to the memory of Peter Carr whose works on volatility modeling have been so inspiring to us. This is joint work with Jordan Lekeufack (UC Berkeley).

- July 2022: new article "Does the Term-Structure of Equity At-the-Money Skew Really Follow a Power Law?" Using two years of S&P 500, Eurostoxx 50, and DAX data, we empirically show that the term-structure of the at-the-money (ATM) skew of equity indexes does not follow a power law for short maturities and is much better captured by simple parametrizations that do not blow up for vanishing maturity. This is joint work with Mehdi El Amrani (Bloomberg L.P.).

- July 2022: new article "Dispersion-Constrained Martingale Schrődinger Bridges: Joint Entropic Calibration of Stochastic Volatility Models to S&P 500 and VIX Smiles". We extend the discrete-time construction of [Guyon, J.: The Joint S&P 500/VIX Smile Calibration Puzzle Solved, Risk, April 2020] and explain how to build a continuous-time stochastic volatility (SV) model which jointly and exactly calibrates S&P 500 (SPX) smiles, VIX futures, and VIX smiles at discrete dates, via minimum entropy.

- My article "The VIX Future in Bergomi Models: Fast Approximation Formulas and Joint Calibration with S&P 500 Skew" has been accepted for publication in SIAM Journal on Financial Mathematics.

- On February 22, 2022 I posted a revision of my article "The VIX Future in Bergomi Models: Fast Approximation Formulas and Joint Calibration with S&P 500 Skew". The paper is about the calibration of stochastic volatility models in general, and Bergomi models in particular (1-factor, 2-factor, and their skewed versions). First I derive new fast approximation formulas for VIX futures and VIX power payoffs in Bergomi models using vol-of-vol expansions. I show that for typical market calibrating parameters, the approximations are very accurate, in particular even for large vol-of-vol. The proofs are based on the exponential generating function of Hermite polynomials. Using those new formulas together with the Bergomi-Guyon expansion allows us to carry out a fast calibration of the 2-factor Bergomi model jointly to the term-structures of S&P 500 ATM skew and implied VIX2 volatility. Very interestingly, the joint fit selects: (1) much larger values of vol-of-vol and mean reversion than those previously reported in the literature, and (2) fully correlated Brownian motions, thus producing a (Markovian) pure path-dependent volatility model with rough-like paths.

- I was an examiner of Shiyi Wang's PhD thesis (Monash University, Melbourne) on optimal transport and calibration in finance.

- On December 14, 2021, Le Monde has published my article Ligue des champions : fallait-il annuler complètement le résultat du premier tirage ? (in French). The article analyzes the bugs that occurred during the draw of the round of 16 of the 2021-22 UEFA Champions League from a probabilistic point of view and explains where the re-draw should have started, instead of the whole first draw being canceled.

- On December 10, 2021 I was interviewed by the French newspaper L'Équipe on how to compute the correct probabilities of the draw of the round of 16 of the UEFA Champions League.

- Le Monde has published my article Ligue des champions : le Real Madrid et Chelsea, adversaires les plus probables du PSG et de Lille on December 10, 2021 (in French). In this op-ed, I explain how to compute the correct probabilities of the draw of the round of 16 of the UEFA Champions League. It is not as easy as it may look like! This year, on top of giving MonteCarlo estimates, I also give the exact probabilities, in a joint work with Cyril Bertrand and Maxim Legendre (Ecole des Ponts).

- On December 7, 2021, at QuantMinds 2021, I presented for the first time this work that I believe is particularly important: "Volatility is (Mostly) Path-Dependent". This is joint work with Jordan Lekeufack (UC Berkeley). Using ML (Lasso and neural networks) on SPX and VIX, we prove that volatility is mostly endogenous: explained only by past asset returns (94+% variance explained by past returns only). And we show that short-term price returns and longer-term squared returns are enough to explain volatility. This not only accounts for important stylized facts: leverage effect, volatility clustering, Zumbach effect. It also quantitatively learns volatility remarkably well. I believe this is the right way of modeling volatility: (1) explain volatility in an endogenous way as best as we can (2) add the (small) exogenous part if needed. Paper to come out soon!

- On November 22, 2021 (Research in Options 2021) and on December 8, 2021 (QuantMinds 2021), I gave a talk entitled "A New Look at Bergomi Models: Closed-Form VIX Futures Expansions, Joint S&P 500/VIX Calibration, and the Appeal of Path-Dependent Volatility". In this talk I present new closed-form approximations for the VIX future in Bergomi models, and show how they can be used together with the so-called Bergomi-Guyon expansion of the SPX smile to jointly calibrate to SPX and VIX. Very interestingly, the joint calibration naturally points to Path-Dependent Volatility. Preprint available here.

- Le Monde has published my op-ed Football : "La FIFA doit revoir le format de la Coupe du monde 2026" (Soccer: FIFA must change the format of the 2026 World Cup) on November 19, 2021 (in French). In this op-ed, I propose a better format made of eight groups of six. In order for the tournament to still fit in one month, each group is divided into two cross-competing subgroups of three. Your comments are most welcome!

- I have recently posted a new article entitled The smile of stochastic volatility: Revisiting the Bergomi-Guyon expansion. The paper revisits the expansion in small volatility of volatility that I have published with Lorenzo Bergomi in 2012, In particular it presents a new, more probabilistic proof of the expansion; introduces the concept of implied spot-variance covariance; and proposes rough-like volatility models in which the at-the-money skew does NOT blow up for vanishing maturities (as the data actually suggests).

- I was interviewed by the Swiss newspaper Le Temps on October 23, 2021 about how sports leagues are scheduled, in particular European soccer leagues.

- My article 'Choose Your Opponent': A New Knockout Design for Hybrid Tournaments has been published in Journal of Sports Analytics. A preprint is also available here.

- On August 26, 2021, Four Four Two has published my article "Champions League group stage draw: who are the most likely opponents of Manchester City, Manchester United, Liverpool and Chelsea?".

- I had the pleasure to organize a minisymposium on "Volatility Modeling: Joint Calibration of S&P 500 and VIX Smiles" during the 2021 SIAM Conference on Financial Mathematics & Engineering. A big thank you to Gregoire Loeper, Mathieu Rosenbaum, and Yuri Saporito for accepting my invitation and for giving great, enlightening talks on this very rich, fascinating topic. Beautiful and ingenuous solutions have been presented that include Schrődinger bridges, nonlinear semimartingale optimal transport, rough volatility, and singular perturbation techniques. The replay of the minisymposium, which took place on June 2, 2021, is already available on the conference platform for registered participants.

- I have posted a new article on Dispersion-Constrained Martingale Schrődinger Problems and the Exact Joint S&P 500/VIX Smile Calibration Puzzle, following up on this article on the exact joint S&P 500/VIX smile calibration problem that I published in Risk in April 2020. This version includes new theorems, proofs, analysis, and numerical tests. In particular it develops a theory of dispersion-constrained martingale Schrődinger problems and proves strong duality results for them.

- On April 26, 2021 I was interviewed by the French newspaper L'Équipe about the almost closedness of the UEFA Champions League and its new format for the 2024-27 cycle. The article was reproduced in the print version dated April 27 under the title "La coupe aux grandes œillères".

- On April 17, 2021, the Croatian newspaper Slobodna Dalmacija has published an article on me and my work on fairness in sports, in particular its impact on major soccer tournaments. Thank you Antonio Juričić for contacting me and for the nice article!

- On April 9, 2021, I won the 2nd prize at the research paper competition of the 2021 MIT Sloan Sports Analytics Conference, the biggest sports analytics event in the world, for my article Risk of Collusion: Will Groups of 3 Ruin the FIFA World Cup?, Journal of Sports Analytics 6(4):259-279, 2020. A big thank you to the organizers and to the two juries (3 semifinal jurors and 3 final jurors) for rewarding my work and rewarding research on tournament design. Tournament design matters! Now, let us convince FIFA to adopt a better, fairer format, less prone to collusion, for example one of the 7 formats that I suggest in the paper.

- I was appointed Associate Editor of Finance & Stochastics on April 1, 2021 for a three-year term. Thank you to the Editor-In-Chief, Martin Schweizer, for honoring me with such an appointment. Glad and proud to join the F&S family!

- I was elected Louis Bachelier Fellow of the Institut Louis Bachelier in February 2021. Thank you to the Fellows for their votes! Glad and proud to join the community of Louis Bachelier Fellows!

- My work on the risk of collusion is highlighted twice in the first section ("Format") of the Wikipedia page on the 2026 FIFA World Cup. Thank you Wiki!