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Quantum Machine Learning methods for Fourier-based distribution estimation with application in option pricing

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  • Fernando Alonso
  • 'Alvaro Leitao
  • Carlos V'azquez

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.

Suggested Citation

  • Fernando Alonso & 'Alvaro Leitao & Carlos V'azquez, 2025. "Quantum Machine Learning methods for Fourier-based distribution estimation with application in option pricing," Papers 2510.19494, arXiv.org.
    • Handle: RePEc:arx:papers:2510.19494
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    References listed on IDEAS

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    1. Dong An & Noah Linden & Jin-Peng Liu & Ashley Montanaro & Changpeng Shao & Jiasu Wang, 2020. "Quantum-accelerated multilevel Monte Carlo methods for stochastic differential equations in mathematical finance," Papers 2012.06283, arXiv.org, revised Jun 2021.
    2. Brian Huge & Antoine Savine, 2020. "Differential Machine Learning," Papers 2005.02347, arXiv.org, revised Sep 2020.
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