Lévy type signature models

14.10.2021 16:45 - 17:30

Francesca Primavera (U Wien)

Abstract: Signature models have recently entered the field of Mathematical Finance. However, despite the presence of jumps in financial data, the signature models for asset prices proposed so far have only dealt with the continuous-path setting. Based on recent results on the signature of càdlàg paths, we define signature-based models which include jumps. The approach that we follow consists of parameterizing the model itself or its characteristics as linear functions of the signature of an augmented Lévy process, interpreted as market’s primary underlying process. We show that, in this contest, first principles, like absence of arbitrage, still apply. Finally, we prove that the signature of a generic ℝd-valued Lévy process is a polynomial process on the extended tensor algebra and derive its expected value via polynomial technology. This result, when applied to the market’s primary process, yields a compact pricing formula, used in the calibration of the model to market data.

This talk is based an ongoing joint work with Christa Cuchiero and Sara Svaluto-Ferro.


HS 5, EG., OMP 1