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A Quantum algorithm for linear PDEs arising in Finance

Author

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  • Filipe Fontanela
  • Antoine Jacquier
  • Mugad Oumgari

Abstract

We propose a hybrid quantum-classical algorithm, originated from quantum chemistry, to price European and Asian options in the Black-Scholes model. Our approach is based on the equivalence between the pricing partial differential equation and the Schrodinger equation in imaginary time. We devise a strategy to build a shallow quantum circuit approximation to this equation, only requiring few qubits. This constitutes a promising candidate for the application of Quantum Computing techniques (with large number of qubits affected by noise) in Quantitative Finance.

Suggested Citation

  • Filipe Fontanela & Antoine Jacquier & Mugad Oumgari, 2019. "A Quantum algorithm for linear PDEs arising in Finance," Papers 1912.02753, arXiv.org, revised Feb 2021.
    • Handle: RePEc:arx:papers:1912.02753
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    File URL: http://arxiv.org/pdf/1912.02753
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    References listed on IDEAS

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    1. Black, Fischer & Scholes, Myron S, 1973. "The Pricing of Options and Corporate Liabilities," Journal of Political Economy, University of Chicago Press, vol. 81(3), pages 637-654, May-June.
    2. C. Brown & J. C. Handley & C.-T. Lin & K. J. Palmer, 2016. "Partial differential equations for Asian option prices," Quantitative Finance, Taylor & Francis Journals, vol. 16(3), pages 447-460, March.
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    Cited by:

    1. Addie, Ron & Taranto, Aldo, 2024. "Economic Similarities and their Application to Inflation," EconStor Preprints 283286, ZBW - Leibniz Information Centre for Economics.
    2. Takayuki Sakuma, 2020. "Application of deep quantum neural networks to finance," Papers 2011.07319, arXiv.org, revised May 2022.
    3. Tianchen Zhao & Chuhao Sun & Asaf Cohen & James Stokes & Shravan Veerapaneni, 2022. "Quantum-inspired variational algorithms for partial differential equations: Application to financial derivative pricing," Papers 2207.10838, arXiv.org.
    4. 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.
    5. Antoine Jacquier & Oleksiy Kondratyev & Gordon Lee & Mugad Oumgari, 2023. "Quantum Computing for Financial Mathematics," Papers 2311.06621, arXiv.org.
    6. Martin Vesely, 2023. "Finding the Optimal Currency Composition of Foreign Exchange Reserves with a Quantum Computer," Papers 2303.01909, arXiv.org.

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