Meetings, workshops and conferences have been cancelled worldwide: senior researcher as well as young PhD students can only interact virtually. To keep the active spirit of our whole scientific community going and to continue solving financial problems of our times, we provide virtual ways of scientific exchange for the time being.

We organise an online talk every second Thursday, alternating with the talks set up by the SIAM activity group on financial mathematics and engineering (

Find the list of the BFS One World Seminars below.

Date: Thursday, 10 September 2020

Speaker: TBA

Title: TBA

Abstract: BA

Thursday, 10 September 2020, 19:00 CEST (Central European Summer Time)

Registration is free but compulsory:

Date: Thursday, 16 July 2020

Speaker: Julien Guyon (Bloomberg L.P., New York)

Title: The Joint S&P 500/VIX Smile Calibration Puzzle Solved

Abstract: Since VIX options started trading in 2006, many researchers have tried to build a model that jointly and exactly calibrates to the prices of S&P 500 (SPX) options, VIX futures and VIX options. So far the best attempts, which used parametric continuous-time jump-diffusion models on the SPX, could only produce approximate fits. In this talk we solve this longstanding puzzle using a completely different approach: a nonparametric discrete-time model. The model is cast as a dispersion-constrained martingale transport problem which is solved using the Sinkhorn algorithm. We prove by duality that the existence of such model means that the SPX and VIX markets are jointly arbitrage-free. The algorithm identifies joint SPX/VIX arbitrages should they arise. Our numerical experiments show that the algorithm performs very well in both low and high volatility environments. Finally, we briefly discuss:
(i) how our technique extends to continuous-time stochastic volatility models;
(ii) a remarkable feature of the SPX and VIX markets: the inversion of convex ordering, and how classical stochastic volatility models can reproduce it;
(iii) why, due to this inversion of convex ordering, and contrary to what has often been stated, among the continuous stochastic volatility models calibrated to the market smile, the Dupire local volatility model does not maximize the price of VIX futures.

Short bio: Julien Guyon is a senior quantitative analyst in the Quantitative Research group at Bloomberg L.P., New York. He is also an adjunct professor in the Department of Mathematics at Columbia University and at the Courant Institute of Mathematical Sciences, NYU. Before joining Bloomberg, Julien worked in the Global Markets Quantitative Research team at Société Générale in Paris for six years (2006-2012), and was an adjunct professor at Université Paris Diderot and Ecole des Ponts ParisTech. He co-authored the book Nonlinear Option Pricing (Chapman & Hall, CRC Financial Mathematics Series, 2014) with Pierre Henry-Labordère. His main research interests include nonlinear problems, volatility and correlation modeling, and numerical probabilistic methods. Julien holds a Ph.D. in Probability Theory and Statistics from Ecole des Ponts ParisTech. He graduated from Ecole Polytechnique (Paris), Université Pierre-et-Marie-Curie (Paris), and Ecole des Ponts ParisTech. A big soccer fan, Julien has also developed a strong interest in sports analytics, and has published several articles on the FIFA World Cup, the UEFA Champions League, and the UEFA Euro in top-tier newspapers such as The New York Times, The Times, Le Monde, and El Pais. Some of his suggestions for draws and competition formats have already been implemented by FIFA and UEFA.

Thursday, 16 July 2020, 19:00 CEST (Central European Summer Time)

Slides to talk:

Date: Thursday, 02 July 2020

Speaker: Xin Guo (University of California Berkeley)

Title: Understanding GANs through MFGs and SDEs approximations

Abstract: Generative Adversarial Networks (GANs) have celebrated great empirical success, especially in image generation and processing. There is a recent surge of interest in GANs to financial applications, including asset pricing, portfolio optimization, and multi-agent market simulation.
In this talk, we will discuss some recent progress in mathematical understanding of GANs. The first is the theoretical connection between GANs and MFGs: interpreting MFGs as GANs, on one hand, allows us to devise GANs-based algorithm to solve high dimensional MFGs. Interpreting GANs as MFGs, on the other hand, provides a new and probabilistic foundation for GANs.
The second is on approximating GANs training in the form of SDEs. This SDEs approximation provides, for the first time, an analytical tool for resolving some well-recognized  issues in the machine learning community for GANs training.

Thursday, 2 July 2020, 19:00 CEST (Central European Summer Time)

Slides to talk:

Date: Thursday, 18 June 2020

Speaker: Peter Tankov (ENSAE Paris)

Title: Environmental Impact Investing: how green-minded investors spur companies to reduce their emissions

Abstract: We develop a dynamic equilibrium model to explain how green investing spurs companies to reduce their greenhouse gas emissions by raising their cost of capital. In the model, two groups of CARA investors with different views on future environmental risks determine the cost of capital for a group of polluting companies, which then play an emission-reduction game to maximize their profits. As a result, companies’ emissions decrease when the proportion of green investors and their environmental stringency increase, as well as when the marginal abatement cost decreases. However, heightened uncertainty about future environmental risks alleviates the pressure on the cost of capital for the most carbon-intensive companies and pushes them to increase their emissions. Consistent with the nature of environmental risks, this uncertainty is modeled as non-Gaussian. We provide empirical evidence supporting our results by focusing on United States stocks and using green fund holdings between 2006 and 2018 to proxy for green investors’ beliefs. When the fraction of assets managed by green investors doubles, companies’ carbon intensity drops by 5% per year.

Joint work with Tiziano De Angelis and Olivier David Zerbib.

Thursday, 18 June 2020, 19:00 CEST (Central European Summer Time)

Link to recorded talk:

Slides to talk:

Date: Thursday, 04 June 2020

Speaker: Nizar Touzi (Ecole Polytechnique Paris)

Title: Is there a Golden Parachute in Sannikov’s principal-agent problem?

Abstract: This paper provides a complete review of the continuous-time optimal contracting problem introduced by Sannikov (2008) in the extended context allowing for possible different discount factors of both parties. The agent’s problem is to seek for optimal effort, given the compensation scheme proposed by the principal over a random horizon. Then, given the optimal agent’s response, the principal determines the best compensation scheme in terms of running payment, retirement, and lump-sum payment at retirement.

A Golden parachute is a situation where the agent ceases any efforts at some positive stopping time, and receives a payment afterwards, possibly consisting of a lump sum and/or a continuous stream of payments. We show that a Golden Parachute only exists in certain specific circumstances. This is in contrast with the results claimed by Sannikov (2008) where the only requirement is a positive agent’s marginal cost of effort at zero. Namely, we show that there is no Golden Parachute if this parameter is too large. Similarly, in the context of a concave marginal utility, there is no Golden Parachute if the agent’s utility function has a too negative curvature at zero.

In the general case, we provide a rigorous analysis of this problem and we prove that an agent with positive reservation utility is either never retired by the principal, or retired above some given threshold (as in Sannikov (2008)’s solution). In particular, different discount factors induce naturally a face-lifted utility function, which allows to reduce the whole analysis to the equal-discount factors setting. Finally, we also confirm that an agent with small reservation utility does have an informational rent, meaning that the principal optimally offers him a contract with strictly higher utility value.

Thursday, 4 June 2020, 19:00 CEST (Central European Summer Time)

Slides to talk:

Date: Thursday, 21 May 2020

Speaker: Jan Obloj (University of Oxford)

Title: Data driven robustness and uncertainty sensitivity analysis

Abstract: In this talk, I will showcase how methods from optimal transport and distributionally robust optimisation allow to capture and quantify sensitivity to model uncertainty for a myriad of problems.
We consider a generic stochastic optimisation problem. This could be a mean-variance or a utility maximisation portfolio allocation problem, an optimised certainty equivalent or a risk measure computation, a standard regression or a deep learning problem. At the heart of the optimisation is a probability measure, or a model, which describes the system. It could come from data, simulation or a modelling effort but there is always a degree of uncertainty about it.
We take a non-parametric approach and capture model uncertainty using Wasserstein balls around the postulated measure. Our main results provide explicit formulae for the first order correction to both the value function and the optimiser. We further extend our results to optimisation under linear constraints. Our sensitivity analysis of the distributionally robust optimisation problems finds applications in statistics, machine learning, mathematical finance and uncertainty quantification.
In the talk, I will discuss several financial examples anchored in a one-step financial model and compute their sensitivity to model uncertainty. These will include: option pricing, mean-variance portfolio selection, optimised certainty equivalent and similar risk assessments as well as a robust version of Davis’ marginal utility option pricing. I will also discuss briefly other applications, such as explicit formulae for first-order approximations of square-root LASSO and square-root Ridge optimisers and measures of NN architecture robustness wrt to adversarial data. I will also showcase the link with building data-driven estimators of risk measures.
Talk based on joint works with Daniel Bartl, Samuel Drapeau and Johannes Wiesel.

Thursday, 21 May 2020, 19:00 CEST (Central European Summer Time)

Slides to talk:

Date: Thursday, 07 May 2020

Speaker: Paul Embrechts (Professor emeritus ETH Zurich)

Title: Operational Risk revisited: from Basel to the coronavirus

Abstract: In the company of market and credit risk, from a more mathematical point of view, operational risk has always been viewed as the “little brother or sister”. And yet as the 2007-2009 Financial Crisis has shown and as we no doubt will find out from the coronavirus crisis sometime in the future, operational risk is an eminently important, and surely technically demanding risk category within the regulatory frameworks of insurance (Solvency 2, say) and banking (the various Basel frameworks). In this talk I will sketch some of its history, some of the main technical modeling tools used and comment on methodological ways forward. I will also discuss some of the early lessons (hopefully) learned from the current coronavirus pandemic.

Thursday, 7 May 2020, 19:00 CEST (Central European Summer Time)

Link to recorded talk:

Slides to talk:

Date: Thursday, 23 April 2020

Speaker: Mathieu Rosenbaum (Ecole Polytechnique, Paris)

Title: Super-Heston rough volatility, Zumbach effect and the Guyon’s conjecture

Abstract: The rough Heston model is known to reproduce accurately the behavior of historical volatility time series as well as the dynamics of the implied volatility surface. However, some argue that actual volatility tails are even fatter than that generated in the rough Heston model. Furthermore, it fails to reproduce a very subtle property of historical data referred to as Zumbach effect. In this talk we address these two concerns introducing so-called super-Heston rough volatility models. It turns out that these models enable us to obtain joint calibration of both SPX and VIX implied volatility surfaces, hence providing a counter-example to a long-standing conjecture by Julien Guyon (this is joint work with Aditi Dandapani, Jim Gatheral and Paul Jusselin).

Thursday, 23 April 2020, 19:00 CEST (Central European Summer Time)