Mathematical Finance
Time: 10.00 am
Date:20th of November 2025
Room 3001

Sara SVALUTO-FERRO (University of Verona) “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 examines the local-in-time expansion of a continuous-time process and its conditional moments, including the characteristic function. By leveraging the time-extended Itôsignature—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.
The second 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.
Joint work with Federico Bandi, Roberto Renò, Christa Cuchiero, Guido Gazzani, Janka Möller.

Organizers:  Roxanna DUMITRESCU – Jean-François CHASSAGNEUX