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

ArXiv ID: 2510.19494 “View on arXiv”

Authors: Fernando Alonso, Álvaro Leitao, Carlos Vázquez

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.

Keywords: quantum machine learning, parametrized quantum circuits, option pricing, Fourier series, quantum accelerated Monte Carlo, Derivatives

Complexity vs Empirical Score

• Math Complexity: 8.5/10
• Empirical Rigor: 4.0/10
• Quadrant: Lab Rats
• Why: The paper exhibits high mathematical density with advanced concepts like quantum circuit approximations and Fourier series, but lacks practical implementation details or real-world data, focusing instead on theoretical models and simulation experiments.

  flowchart TD
    A["Research Goal: Hybrid Quantum-Classical<br/>methods for Option Pricing"] --> B["Data: Market/Underlying Asset Data"]
    B --> C["Methodology: Quantum Machine Learning<br/>using Parametrized Quantum Circuits"]
    C --> D["Process: Fourier Series Reconstruction<br/>of Statistical Distributions"]
    D --> E["Benchmark: Quantum Accelerated Monte Carlo<br/>QAMC"]
    E --> F{"Analysis & Evaluation"}
    F --> G["Outcome: High Accuracy<br/>Low Computational Cost"]
    F --> H["Outcome: Competitive Quantum Alternative<br/>for Derivatives Valuation"]