Signature-based models: theory, calibration, and expansions
Abstract
Signature methods provide a non-parametric approach to extracting features from trajectories, offering versatile applications in finance. The structure of signature components enables the use of advanced mathematical tools and the construction of highly general models capable of capturing diverse behaviors. In this talk, we introduce the concept of the signature and its key properties, illustrating its potential through two financial applications. The first application focuses on a stochastic volatility model where volatility dynamics are described by linear functions of the (time-extended) signature of a primary process. When this process is of polynomial type, its truncated signature retains this structure, allowing for closed-form expressions of the squared VIX. By incorporating the Brownian motion driving the stock price, both the log-price and the squared VIX can be expressed linearly in terms of the signature of the augmented process, achieving highly accurate calibration results for SPX and VIX options. The second application examines the local-in-time expansion of a continuous-time process and its conditional moments, including the characteristic function. By leveraging the time-extended Itô signature—composed of iterated integrals of deterministic and stochastic signals (time, multiple correlated Brownian motions, and compound Poisson processes)—we derive automated expansions to any order with explicit coefficients. This provides stochastic representations suitable for asymptotic analysis in the short-time limit.
Watch recording ↗About the speaker
Sara Svaluto-Ferro is an Associate Professor at the University of Verona, Department of Economics, specializing in mathematical methods for economics and finance. Previously, she was an Assistant Professor (RTDB) at the same department and a postdoctoral researcher at the University of Vienna in the research group of Prof. C. Cuchiero. She earned her PhD in Mathematics from ETH Zurich under the supervision of Prof. M. Larsson. Her research focuses on stochastic processes, including affine and polynomial models, stochastic representations of PDEs, and optimization in infinite-dimensional spaces, with applications in financial mathematics, systemic risk, and rough volatility modeling. In the last years she dedicated particular attention to applications of signature processes in finance.