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Quantum computing for multidimensional option pricing: End-to-end pipeline

Author

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  • Julien Hok
  • 'Alvaro Leitao

Abstract

This work introduces an end-to-end framework for multi-asset option pricing that combines market-consistent risk-neutral density recovery with quantum-accelerated numerical integration. We first calibrate arbitrage-free marginal distributions from European option quotes using the Normal Inverse Gaussian (NIG) model, leveraging its analytical tractability and ability to capture skewness and fat tails. Marginals are coupled via a Gaussian copula to construct joint distributions. To address the computational bottleneck of the high-dimensional integration required to solve the option pricing formula, we employ Quantum Accelerated Monte Carlo (QAMC) techniques based on Quantum Amplitude Estimation (QAE), achieving quadratic convergence improvements over classical Monte Carlo (CMC) methods. Theoretical results establish accuracy bounds and query complexity for both marginal density estimation (via cosine-series expansions) and multidimensional pricing. Empirical tests on liquid equity entities (Credit Agricole, AXA, Michelin) confirm high calibration accuracy and demonstrate that QAMC requires 10-100 times fewer queries than classical methods for comparable precision. This study provides a practical route to integrate arbitrage-aware modelling with quantum computing, highlighting implications for scalability and future extensions to complex derivatives.

Suggested Citation

  • Julien Hok & 'Alvaro Leitao, 2026. "Quantum computing for multidimensional option pricing: End-to-end pipeline," Papers 2601.04049, arXiv.org.
    • Handle: RePEc:arx:papers:2601.04049
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    References listed on IDEAS

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    1. Fang, Fang & Oosterlee, Kees, 2008. "A Novel Pricing Method For European Options Based On Fourier-Cosine Series Expansions," MPRA Paper 9319, University Library of Munich, Germany.
    2. Breeden, Douglas T & Litzenberger, Robert H, 1978. "Prices of State-contingent Claims Implicit in Option Prices," The Journal of Business, University of Chicago Press, vol. 51(4), pages 621-651, October.
    3. 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.
    4. Hadrien de March & Pierre Henry-Labordere, 2019. "Building Arbitrage-Free Implied Volatility: Sinkhorn'S Algorithm And Variants," Working Papers hal-02011533, HAL.
    5. Bertrand Tavin, 2012. "Implied Distribution as a Function of the Volatility Smile," Post-Print hal-02313144, HAL.
    6. Jim Gatheral & Antoine Jacquier, 2014. "Arbitrage-free SVI volatility surfaces," Quantitative Finance, Taylor & Francis Journals, vol. 14(1), pages 59-71, January.
    7. Julien Hok & Tat Lung Chan, 2016. "Option pricing with Legendre polynomials," Papers 1610.03086, arXiv.org, revised Mar 2017.
    8. Koichi Maekawa & Ken-ichi Kawai, 2004. "Option pricing under NIG distribution: --- The empirical analysis of Nikkei 225 option ----," Econometric Society 2004 Far Eastern Meetings 607, Econometric Society.
    9. Fernández, J.L. & Ferreiro, A.M. & García-Rodríguez, J.A. & Leitao, A. & López-Salas, J.G. & Vázquez, C., 2013. "Static and dynamic SABR stochastic volatility models: Calibration and option pricing using GPUs," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 94(C), pages 55-75.
    10. Julien Hok & Shih-Hau Tan, 2019. "Calibration of local volatility model with stochastic interest rates by efficient numerical PDE methods," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 42(2), pages 609-637, December.
    11. Heston, Steven L, 1993. "A Closed-Form Solution for Options with Stochastic Volatility with Applications to Bond and Currency Options," The Review of Financial Studies, Society for Financial Studies, vol. 6(2), pages 327-343.
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