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Universal approximation on non-geometric rough paths and applications to financial derivatives pricing

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  • Fabian A. Harang
  • Fred Espen Benth
  • Fride Straum

Abstract

We present a novel perspective on the universal approximation theorem for rough path functionals, introducing a polynomial-based approximation class. We extend universal approximation to non-geometric rough paths within the tensor algebra. This development addresses critical needs in finance, where no-arbitrage conditions necessitate It\^o integration. Furthermore, our findings motivate a hypothesis for payoff functionals in financial markets, allowing straightforward analysis of signature payoffs proposed in \cite{arribas2018derivativespricingusingsignature}.

Suggested Citation

  • Fabian A. Harang & Fred Espen Benth & Fride Straum, 2024. "Universal approximation on non-geometric rough paths and applications to financial derivatives pricing," Papers 2412.16009, arXiv.org, revised Dec 2025.
    • Handle: RePEc:arx:papers:2412.16009
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    References listed on IDEAS

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    1. Terry Lyons & Sina Nejad & Imanol Perez Arribas, 2019. "Numerical Method for Model-free Pricing of Exotic Derivatives in Discrete Time Using Rough Path Signatures," Applied Mathematical Finance, Taylor & Francis Journals, vol. 26(6), pages 583-597, November.
    2. Hélyette Geman & Marc Yor, 1993. "Bessel Processes, Asian Options, And Perpetuities," Mathematical Finance, Wiley Blackwell, vol. 3(4), pages 349-375, October.
    3. Fred Espen Benth & Silvia Lavagnini, 2019. "Correlators of Polynomial Processes," Papers 1906.11320, arXiv.org, revised Apr 2021.
    4. Bennedsen, Mikkel, 2017. "A rough multi-factor model of electricity spot prices," Energy Economics, Elsevier, vol. 63(C), pages 301-313.
    5. Christa Cuchiero & Sara Svaluto-Ferro, 2021. "Infinite-dimensional polynomial processes," Finance and Stochastics, Springer, vol. 25(2), pages 383-426, April.
    6. Benth, Fred Espen & Saltyte Benth, Jurate, 2009. "Dynamic pricing of wind futures," Energy Economics, Elsevier, vol. 31(1), pages 16-24, January.
    7. Fred Espen Benth, 2021. "Pricing of Commodity and Energy Derivatives for Polynomial Processes," Mathematics, MDPI, vol. 9(2), pages 1-30, January.
    8. Larsson, Karl & Green, Rikard & Benth, Fred Espen, 2023. "A stochastic time-series model for solar irradiation," Energy Economics, Elsevier, vol. 117(C).
    9. 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.
    10. Christa Cuchiero & Francesca Primavera & Sara Svaluto-Ferro, 2022. "Universal approximation theorems for continuous functions of c\`adl\`ag paths and L\'evy-type signature models," Papers 2208.02293, arXiv.org, revised Aug 2023.
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