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

TL;DR

This paper introduces hybrid classical-quantum methods utilizing Quantum Machine Learning to estimate distributions for option pricing, demonstrating high accuracy and competitiveness with traditional techniques.

Contribution

It presents novel hybrid quantum-classical algorithms based on Fourier series reconstruction from QML outputs for financial derivative pricing.

Findings

Achieves high accuracy in Fourier coefficient estimation.

Demonstrates competitive performance against Quantum Accelerated Monte Carlo.

Shows potential for quantum methods to improve derivative valuation efficiency.

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.