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Towards Quantum Advantage in Financial Market Risk using Quantum Gradient Algorithms

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  • Nikitas Stamatopoulos
  • Guglielmo Mazzola
  • Stefan Woerner
  • William J. Zeng

Abstract

We introduce a quantum algorithm to compute the market risk of financial derivatives. Previous work has shown that quantum amplitude estimation can accelerate derivative pricing quadratically in the target error and we extend this to a quadratic error scaling advantage in market risk computation. We show that employing quantum gradient estimation algorithms can deliver a further quadratic advantage in the number of the associated market sensitivities, usually called greeks. By numerically simulating the quantum gradient estimation algorithms on financial derivatives of practical interest, we demonstrate that not only can we successfully estimate the greeks in the examples studied, but that the resource requirements can be significantly lower in practice than what is expected by theoretical complexity bounds. This additional advantage in the computation of financial market risk lowers the estimated logical clock rate required for financial quantum advantage from Chakrabarti et al. [Quantum 5, 463 (2021)] by a factor of ~7, from 50MHz to 7MHz, even for a modest number of greeks by industry standards (four). Moreover, we show that if we have access to enough resources, the quantum algorithm can be parallelized across 60 QPUs, in which case the logical clock rate of each device required to achieve the same overall runtime as the serial execution would be ~100kHz. Throughout this work, we summarize and compare several different combinations of quantum and classical approaches that could be used for computing the market risk of financial derivatives.

Suggested Citation

  • Nikitas Stamatopoulos & Guglielmo Mazzola & Stefan Woerner & William J. Zeng, 2021. "Towards Quantum Advantage in Financial Market Risk using Quantum Gradient Algorithms," Papers 2111.12509, arXiv.org, revised Jul 2022.
  • Handle: RePEc:arx:papers:2111.12509
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    Cited by:

    1. Raphael Auer & Angela Dupont & Leonardo Gambacorta & Joon Suk Park & Koji Takahashi & Andras Valko, 2024. "Quantum computing and the financial system: opportunities and risks," BIS Papers, Bank for International Settlements, number 149.
    2. Abha Naik & Esra Yeniaras & Gerhard Hellstern & Grishma Prasad & Sanjay Kumar Lalta Prasad Vishwakarma, 2023. "From Portfolio Optimization to Quantum Blockchain and Security: A Systematic Review of Quantum Computing in Finance," Papers 2307.01155, arXiv.org.
    3. Yen-Jui Chang & Wei-Ting Wang & Hao-Yuan Chen & Shih-Wei Liao & Ching-Ray Chang, 2023. "Preparing random state for quantum financing with quantum walks," Papers 2302.12500, arXiv.org, revised Mar 2023.
    4. Yen-Jui Chang & Wei-Ting Wang & Hao-Yuan Chen & Shih-Wei Liao & Ching-Ray Chang, 2023. "A novel approach for quantum financial simulation and quantum state preparation," Papers 2308.01844, arXiv.org, revised Apr 2024.

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