Quantum Machine Learning Estimates Fourier-based Distributions for Option Pricing, Assessed Against Accelerated Monte Carlo Techniques

Quantum Physics arXiv:2510.19494 (quant-ph) [Submitted on 22 Oct 2025] Title:Quantum Machine Learning methods for Fourier-based distribution estimation with application in option pricing Authors:Fernando Alonso, Álvaro Leitao, Carlos Vázquez View a PDF of the paper titled Quantum Machine Learning methods for Fourier-based distribution estimation with application in option pricing, by Fernando Alonso and 1 other authors View PDF HTML (experimental) Abstract:The ongoing progress in quantum technologies has fueled a sustained exploration of their potential applications across various domains. One particularly promising field is quantitative finance, where a central challenge is the pricing of financial derivatives-traditionally addressed through Monte Carlo integration techniques. In this work, we introduce two hybrid classical-quantum methods to address the option pricing problem. These approaches rely on reconstructing Fourier series representations of statistical distributions from the outputs of Quantum Machine Learning (QML) models based on Parametrized Quantum Circuits (PQCs). We analyze the impact of data size and PQC dimensionality on performance.

Quantum Accelerated Monte Carlo (QAMC) is employed as a benchmark to quantitatively assess the proposed models in terms of computational cost and accuracy in the extraction of Fourier coefficients. Through the numerical experiments, we show that the proposed methods achieve remarkable accuracy, becoming a competitive quantum alternative for derivatives valuation. Comments: Subjects: Quantum Physics (quant-ph); Representation Theory (math.RT); Computational Finance (q-fin.CP) MSC classes: 65C05, 65R20, 42A10, 81P68 Cite as: arXiv:2510.19494 [quant-ph] (or arXiv:2510.19494v1 [quant-ph] for this version) https://doi.org/10.48550/arXiv.2510.19494 Focus to learn more arXiv-issued DOI via DataCite (pending registration) Submission history From: Álvaro Leitao Rodriguez [view email] [v1] Wed, 22 Oct 2025 11:43:08 UTC (680 KB) Full-text links: Access Paper: View a PDF of the paper titled Quantum Machine Learning methods for Fourier-based distribution estimation with application in option pricing, by Fernando Alonso and 1 other authorsView PDFHTML (experimental)TeX Source view license Current browse context: quant-ph new | recent | 2025-10 Change to browse by: math math.RT q-fin q-fin.CP References & Citations INSPIRE HEP NASA ADSGoogle Scholar Semantic Scholar export BibTeX citation Loading... BibTeX formatted citation × loading... Data provided by: Bookmark Bibliographic Tools Bibliographic and Citation Tools Bibliographic Explorer Toggle Bibliographic Explorer (What is the Explorer?) Connected Papers Toggle Connected Papers (What is Connected Papers?) Litmaps Toggle Litmaps (What is Litmaps?) scite.ai Toggle scite Smart Citations (What are Smart Citations?) Code, Data, Media Code, Data and Media Associated with this Article alphaXiv Toggle alphaXiv (What is alphaXiv?) Links to Code Toggle CatalyzeX Code Finder for Papers (What is CatalyzeX?) DagsHub Toggle DagsHub (What is DagsHub?) GotitPub Toggle Gotit.pub (What is GotitPub?) Huggingface Toggle Hugging Face (What is Huggingface?) Links to Code Toggle Papers with Code (What is Papers with Code?) ScienceCast Toggle ScienceCast (What is ScienceCast?) Demos Demos Replicate Toggle Replicate (What is Replicate?) Spaces Toggle Hugging Face Spaces (What is Spaces?) Spaces Toggle TXYZ.AI (What is TXYZ.AI?) Related Papers Recommenders and Search Tools Link to Influence Flower Influence Flower (What are Influence Flowers?) Core recommender toggle CORE Recommender (What is CORE?) Author Venue Institution Topic About arXivLabs arXivLabs: experimental projects with community collaborators arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website. Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them. Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs. Which authors of this paper are endorsers? | Disable MathJax (What is MathJax?)