Main Conference Day ThreeThursday, 19 November 2026 - GMT (Greenwich Mean Time, GMTZ)

The SABR model is a cornerstone of interest rate volatility modeling, but its practical application relies heavily on the analytical approximation by Hagan et al., whose accuracy deteriorates for high volatility, long maturities, and out-of-the-money options, admitting arbitrage. While machine learning approaches have been proposed to overcome these limitations, they have often been limited by simplified SABR dynamics or a lack of systematic validation against the full spectrum of market conditions. We develop a novel SABR DNN, a specialized Artificial Deep Neural Network (DNN) architecture that learns the true SABR stochastic dynamics using an unprecedented large training dataset (more than 200 million points) of interest rate Cap/Floor volatility surfaces, including very long maturities (30Y) and extreme strikes consistently with market quotations. Our dataset is obtained via high-precision unbiased Monte Carlo simulation of a special scaled shifted-SABR stochastic dynamics, which allows dimensional reduction without any loss of generality. Our SABR DNN provides arbitrage-free calibration of real market volatility surfaces and Cap/Floor prices for any maturity and strike with negligible computational effort and without retraining across business dates. Our results fully address the gaps in the previous machine learning SABR literature in a systematic and self-consistent way, and can be extended to cover any interest rate European options in different rate tenors and currencies, thus establishing a comprehensive functional SABR framework that can be adopted for daily trading and risk management activities.

Convex volatility interpolation (CVI) casts the problem of fitting arbitrage-free implied volatility surfaces as quadratic programming in variance space. It introduces a dual parametrisation in cubic spline and B-spline spaces, mapping intuitive, dimensionless parameters to the weights of basis functions. Static arbitrage constraints, butterfly and calendar spread, are enforced through linear inequalities. This paper derives and linearises the no-butterfly-arbitrage constraints within the CVI cubic spline parameter space. Notably, the no-butterfly-arbitrage condition is derived in closed form in the linear variance extrapolation region beyond the edge knots. The formulation is model-free, bid-ask-aware, and requires no hyperparameter tuning, working consistently across underlyings. Convexity guarantees a unique global optimum, eliminating the calibration fragility of parametric approaches. Using the Clarabel conic solver, CVI fits the full S&P 500 surface, 14,500 bid-ask quotes across 46 expiries, in 0.15 seconds.

Exponentially weighted moving averages (EWMAs) are ubiquitous in quantitative finance and time series models. Their main limitation is their linear structure. In this talk, we introduce fading memory signatures, a nonlinear extension of EWMAs inspired by the theory of path signatures.

Fading memory signatures provide a flexible framework for learning relationships between sequential inputs and outputs while retaining the fading-memory property of classical EWMAs. They enjoy a universality property analogous to that of polynomials in finite-dimensional regression, making them a natural tool for nonlinear learning from time series data.

We illustrate their versatility in volatility modeling through two applications: (i) regression of volatility indices (VIX, VSTOXX, ...) on the return history of the underlying assets, obtaining remarkably accurate fits, (ii) a new class of volatility models in which volatility is parameterized by fading memory signatures ; this framework naturally includes multifactor Bergomi and Quintic volatility models as special cases while incorporating memory effects in a flexible way for the joint calibration of SPX and VIX derivatives, and more realistic volatility dynamics (Skew Stickiness Ratio).