7 papers
Expected signatures via partial integration, coordinate change and symmetrization
Paul P. Hager, Luca Pelizzari
We study signature transformations of heterogeneous paths whose components may differ in regularity and probabilistic structure. We introduce an invertible change of coor…
The Volterra signature
Paul P. Hager, Fabian N. Harang, Luca Pelizzari +1
Modern approaches for learning from non-Markovian time series, such as recurrent neural networks, neural controlled differential equations or transformers, typically rely on implic…
Computational aspects of the Volterra Signature
Paul P. Hager, Fabian N. Harang, Luca Pelizzari +1
The Volterra signature extends the classical path signature by incorporating general matrix-valued kernel into its iterated integral structure, yielding a flexible notion of memory…
Local regression on path spaces with signature metrics
Christian Bayer, Davit Gogolashvili, Luca Pelizzari
We study nonparametric regression and classification for path-valued data. We introduce a functional Nadaraya-Watson estimator that combines the signature transform from rough path…
Pricing American options under rough volatility using deep-signatures and signature-kernels
Christian Bayer, Luca Pelizzari, Jia-Jie Zhu
We extend the signature-based primal and dual solutions to the optimal stopping problem recently introduced in [Bayer et al.: Primal and dual optimal stopping with signatures, to a…
Rough PDEs for local stochastic volatility models
Peter Bank, Christian Bayer, Peter K. Friz +1
In this work, we introduce a novel pricing methodology in general, possibly non-Markovian local stochastic volatility (LSV) models. We observe that by conditioning the LSV dynamics…