Columbia-NYU Financial Engineering Colloquium: Martin Larsson and Grégoire Loeper
RSVP
Martin Larsson
Professor in the Department of Mathematical Sciences at Carnegie Mellon University
Title
Large-scale dynamics of equity markets of variable size
Abstract
Stochastic portfolio theory (SPT) is concerned with the dynamic properties of large equity markets, especially over long time horizons. While the theoretical literature is well developed, the empirical literature is much less so (with some notable exceptions). In this work, we perform an empirical analysis of the large-scale behavior of the U.S. public equity universe, with a focus on the role of listing and delisting events. Such events have a profound impact on the distribution of capital. They can also produce severe biases in various statistical procedures that do not take these events into account. This phenomenon explains certain counterintuitive results that can arise when standard SPT models are calibrated to observed volatilities, collision rates, and long-term capital distributions. We develop procedures that correct for these biases, and find that our corrected estimates are remarkably consistent with the relationship between volatilities, local correlations, collision rates, and particle densities predicted by very simple diffusion models. Finally, we identify a mechanism by which listings and delistings can stabilize an otherwise unstable particle system. This is joint work with David Itkin and Licheng Zhang.
Bio
Martin Larsson is a professor in the Department of Mathematical Sciences at Carnegie Mellon University, working in mathematical finance, probability theory, stochastic analysis, and statistics. His research has applications to term structure modeling, stochastic portfolio theory, equilibrium analysis, and the statistical analysis of sequentially observed financial data. Before joining CMU in 2019, he was an Assistant Professor of Mathematical Finance at the Department of Mathematics at ETH Zurich. He holds a PhD in Operations Research and Information Engineering from Cornell University, and was a postdoctoral fellow at the Swiss Finance Institute at EPFL in Lausanne. He represents the Department of Mathematical Sciences on the Steering Committee of the Master of Science in Computational Finance (MSCF) program at CMU.
Grégoire Loeper
Senior Scientific Advisor, BNP Paribas and CEO, genOTC
Title
Black, Scholes, Legendre, and Sinkhorn
Abstract
This talk will be a unified overview of some recent and less recent contributions in derivatives pricing. The financial topics are option pricing with market impact and model calibration. The mathematical tools are fully non-linear partial differential equations and martingale optimal transport. Some new and fun (?) results will be a Black-Scholes-Legendre formula for option pricing with market impact, a Martingale Sinkhorn algorithm for martingale optimal transport, a new point of view on the Bass Martingale, and some algorithms for exact local volatility calibration.
Bio
Grégoire Loeper has spent his career between academia and industry, moving between pure mathematics and quantitative finance over the past two decades.
A former student of the École Normale Supérieure in Paris, he received his PhD in 2003 under the supervision of Yann Brenier, one of the founders of modern optimal transport theory. His early work belongs to the core of optimal transport theory and nonlinear PDEs, focusing on the regularity of optimal transport maps, and on well-known equations of fluid mechanics, where he obtained new uniqueness results based on OT.
In 2006, he moved to BNP Paribas, and since then has been active in the derivatives industry for twenty years, as a practitioner, and publishing papers on various areas of mathematical finance (pricing with market impact, statistical trading, model calibration… )
From 2015 to 2020, he returned to academia as Professor at Monash University in Melbourne, where he led the creation of a quantitative finance program. Since his return to France, he has been a Senior Scientific Advisor at BNP Paribas Global Markets.
He is also the Founder & CEO of genOTC, a Paris-based fintech startup launched in 2024. genOTC offers a volatility calibration platform for derivatives pricing professionals, built on his work on stochastic optimal transport.