Universal approximation on non-geometric rough paths and applications to financial derivatives pricing
Fuente:
arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866914211354902528 |
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| author | Harang, Fabian A. Benth, Fred Espen Straum, Fride |
| author_facet | Harang, Fabian A. Benth, Fred Espen Straum, Fride |
| contents | 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 Itô integration. Furthermore, our findings motivate a hypothesis for payoff functionals in financial markets, allowing straightforward analysis of signature payoffs proposed in \cite{arribas2018derivativespricingusingsignature}. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_16009 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Universal approximation on non-geometric rough paths and applications to financial derivatives pricing Harang, Fabian A. Benth, Fred Espen Straum, Fride Functional Analysis Probability Pricing of Securities 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 Itô integration. Furthermore, our findings motivate a hypothesis for payoff functionals in financial markets, allowing straightforward analysis of signature payoffs proposed in \cite{arribas2018derivativespricingusingsignature}. |
| title | Universal approximation on non-geometric rough paths and applications to financial derivatives pricing |
| topic | Functional Analysis Probability Pricing of Securities |
| url | https://arxiv.org/abs/2412.16009 |