2022/08/03 by Christa Cuchiero, Cuchiero, Christa, Francesca Primavera +3 · 4 citations
Economics, Econometrics and Finance · Mathematics · #60J76 #60L10 #FOS: Economics and business #FOS: Mathematics #Financial Risk and Volatility Modeling #Markov Chains and Monte Carlo Methods #Mathematical Finance (q-fin.MF) #Probability (math.PR) #Stochastic processes and financial applications
paper · pdf · doi:10.48550/arxiv.2208.02293
openalex publication_date 2022/08/03 · openalex created_date 2022/08/06 · openalex updated_date 2026/07/28
We prove a universal approximation theorem that allows to approximate continuous functionals of càdlàg (rough) paths uniformly in time and on compact sets of paths via linear functionals of their time-extended signature. Our main motivation to treat this question comes from signature-based models for finance that allow for the inclusion of jumps. Indeed, as an important application, we define a new class of universal signature models based on an augmented Lévy process, which we call Lévy-type signature models. They extend continuous signature models for asset prices as proposed e.g. by Arribas et al.(2020) in several directions, while still preserving universality and tractability properties. To analyze this, we first show that the signature process of a generic multivariate Lévy process is a polynomial process on the extended tensor algebra and then use this for pricing and hedging approaches within Lévy-type signature models.