Signature-Based Models in Finance

Christa Cuchiero (), Guido Gazzani (), Janka Möller () and Sara Svaluto-Ferro ()
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Christa Cuchiero: Vienna University
Guido Gazzani: University of Verona
Janka Möller: Vienna University
Sara Svaluto-Ferro: University of Verona

A chapter in Signature Methods in Finance, 2026, pp 227-264 from Springer

Abstract: Abstract We consider two classes of asset price models where either the price or the volatility dynamics are described by a linear function of the (time extended) signature of a primary process, in general a multidimensional continuous semimartingale. These model classes are universal in the sense that classical models can be approximated arbitrarily well or are simply nested in our setup. Under the additional assumption that the primary process is polynomial, we obtain tractable option pricing formulas for so-called sig-payoffs in the first class and closed form expressions for the VIX squared and the log-price in the second one. In both cases the signature samples can be easily precomputed, hence the calibration task can be split into an offline sampling and a standard optimization. We present several applications, in particular the successfully solved joint SPX/VIX calibration problem.

Date: 2026
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DOI: 10.1007/978-3-031-97239-3_7

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