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

2025-10-22

AI Summary

To address the high computational cost and limited accuracy of Monte Carlo methods in financial derivative pricing, this paper proposes two hybrid quantum-machine-learning algorithms. These methods employ parameterized quantum circuits to directly learn the Fourier-series representation of the underlying asset’s probability distribution, coupled with classical optimization for efficient distribution reconstruction and option price estimation. The key innovation lies in the first-ever deep integration of quantum circuit outputs with Fourier-based distribution estimation—using quantum-accelerated Monte Carlo as a benchmark—thereby significantly improving both the precision of Fourier coefficient extraction and convergence speed while preserving theoretical rigor. Numerical experiments demonstrate consistent superiority over classical Monte Carlo across varying data scales and quantum circuit depths, highlighting practical potential in both computational efficiency and estimation accuracy.

Technology Category

• Machine Learning: Quantum Machine Learning
• Search and Optimization: Learning to Search
• Reasoning under Uncertainty: Stochastic Optimization

Application Category

• Economics, Online Markets and Human Computation: Cost models of using LLMs in production systems
• Graph Algorithms and Modeling for the Web: Graph embeddings and representation learning for Web-related graphs
• Security and Privacy: Large-scale security measurements

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.

Problem

• Developing hybrid classical-quantum methods for option pricing
• Reconstructing Fourier series distributions using quantum machine learning
• Assessing computational cost and accuracy in derivatives valuation

Innovation

• Hybrid classical-quantum methods for option pricing
• Fourier series reconstruction using Quantum Machine Learning
• Parametrized Quantum Circuits for distribution estimation