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Local signature-based expansions

Author

Listed:
  • Federico M. Bandi
  • Roberto Ren`o
  • Sara Svaluto-Ferro

Abstract

We study the local (in time) expansion of a continuous-time process and its conditional moments, including the process' characteristic function. The expansions are conducted by using the properties of the (time-extended) Ito signature, a tractable basis composed of iterated integrals of the driving deterministic and stochastic signals: time, multiple correlated Brownian motions and multiple correlated compound Poisson processes. We show that these properties are conducive to automated expansions to any order with explicit coefficients and, therefore, to stochastic representations in which asymptotics can be conducted for a shrinking time (t to 0), as in the extant continuous-time econometrics literature, but, also, for a fixed time (such that t smaller than 1) with a diverging expansion order. The latter design opens up novel opportunities for identifying deep characteristics of the assumed process.

Suggested Citation

  • Federico M. Bandi & Roberto Ren`o & Sara Svaluto-Ferro, 2025. "Local signature-based expansions," Papers 2504.06351, arXiv.org.
    • Handle: RePEc:arx:papers:2504.06351
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    References listed on IDEAS

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    1. Jos'e E. Figueroa-L'opez & Yankeng Luo & Cheng Ouyang, 2011. "Small-time expansions for local jump-diffusion models with infinite jump activity," Papers 1108.3386, arXiv.org, revised Jul 2014.
    2. Emiel Lemahieu & Kris Boudt & Maarten Wyns, 2023. "Generating drawdown-realistic financial price paths using path signatures," Papers 2309.04507, arXiv.org.
    3. Erdinc Akyildirim & Matteo Gambara & Josef Teichmann & Syang Zhou, 2023. "Randomized Signature Methods in Optimal Portfolio Selection," Papers 2312.16448, arXiv.org.
    4. Eduardo Abi Jaber & Louis-Amand G'erard, 2024. "Signature volatility models: pricing and hedging with Fourier," Papers 2402.01820, arXiv.org, revised Jun 2025.
    5. Terry Lyons & Sina Nejad & Imanol Perez Arribas, 2020. "Non-parametric Pricing and Hedging of Exotic Derivatives," Applied Mathematical Finance, Taylor & Francis Journals, vol. 27(6), pages 457-494, November.
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