Innovation Rooted in a Centuries-Old Problem

Optimal Transport (OT) originated in 1781 with Gaspard Monge, who posed the problem of optimally moving mass between distributions. In the 1940s, Leonid Kantorovich, reformulated the problem using linear programming, making the problem solvable and earning a Nobel Prize for its economic implications.

OT has since become a cornerstone of modern applied mathematics, powering advances in machine learning, image analysis, dynamics and probability theory. At its core, OT provides a principled way to compare and map probability distributions while minimizing a transport cost.

Major contributors to 21st-century advances include J-D. Benamou, Yann Brenier, Alessio Figalli, Wilfrid Gangbo, Gregoire Loeper, Robert McCann, Gabriel Peyré, Vladimir Sudakov, Cédric Villani, and many others.

Volatility calibration has been a core challenge in financial markets since the development of option pricing models in the 1970s. Unlike price, volatility is not directly observable—it must be inferred from market data, particularly from option prices. Accurately capturing its dynamics is essential for derivatives pricing, risk management, and volatility trading strategies.

Volatility is tricky—it changes with market conditions and can behave very differently depending on the option’s strike or maturity. Because of this, we need models to capture how it moves. But here’s the catch: we can’t observe volatility directly. We only see clues about it through option prices. These prices often form patterns—like the market smile—that reflect how complicated volatility really is.

The goal is to find a model that can match this pattern. This process, called calibration, is key for anyone who wants to price derivatives accurately. While many methods have been around for decades, we take a fresh approach. Instead of just minimizing pricing errors, our approach thinks of calibration as aligning two distributions—what we see in the market, and what our model predicts.