Option Pricing using Quantum Computers

Nikitas Stamatopoulos; Daniel J. Egger; Yue Sun; Christa Zoufal; Raban Iten; Ning Shen; Stefan Woerner

doi:10.22331/q-2020-07-06-291

Option Pricing using Quantum Computers

Nikitas Stamatopoulos¹, Daniel J. Egger², Yue Sun¹, Christa Zoufal^2,3, Raban Iten^2,3, Ning Shen¹, and Stefan Woerner²

¹Quantitative Research, JPMorgan Chase & Co., New York, NY, 10017
²IBM Quantum, IBM Research – Zurich
³ETH Zurich

Published:	2020-07-06, volume 4, page 291
Eprint:	arXiv:1905.02666v5
Doi:	https://doi.org/10.22331/q-2020-07-06-291
Citation:	Quantum 4, 291 (2020).

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Abstract

We present a methodology to price options and portfolios of options on a gate-based quantum computer using amplitude estimation, an algorithm which provides a quadratic speedup compared to classical Monte Carlo methods. The options that we cover include vanilla options, multi-asset options and path-dependent options such as barrier options. We put an emphasis on the implementation of the quantum circuits required to build the input states and operators needed by amplitude estimation to price the different option types. Additionally, we show simulation results to highlight how the circuits that we implement price the different option contracts. Finally, we examine the performance of option pricing circuits on quantum hardware using the IBM Q Tokyo quantum device. We employ a simple, yet effective, error mitigation scheme that allows us to significantly reduce the errors arising from noisy two-qubit gates.

Featured image: Probability distribution represented on a quantum register and the payoff function for a European call option, inputs to the algorithm enabling its pricing on a quantum computer.

► BibTeX data

@article{Stamatopoulos2020optionpricingusing,
  doi = {10.22331/q-2020-07-06-291},
  url = {https://doi.org/10.22331/q-2020-07-06-291},
  title = {Option {P}ricing using {Q}uantum {C}omputers},
  author = {Stamatopoulos, Nikitas and Egger, Daniel J. and Sun, Yue and Zoufal, Christa and Iten, Raban and Shen, Ning and Woerner, Stefan},
  journal = {{Quantum}},
  issn = {2521-327X},
  publisher = {{Verein zur F{\"{o}}rderung des Open Access Publizierens in den Quantenwissenschaften}},
  volume = {4},
  pages = {291},
  month = jul,
  year = {2020}
}

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[63] Dylan Herman, Cody Googin, Xiaoyuan Liu, Yue Sun, Alexey Galda, Ilya Safro, Marco Pistoia, and Yuri Alexeev, "Quantum computing for finance", Nature Reviews Physics 5 8, 450 (2023).

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[65] Samuel Mugel, Carlos Kuchkovsky, Escolástico Sánchez, Samuel Fernández-Lorenzo, Jorge Luis-Hita, Enrique Lizaso, and Román Orús, "Dynamic portfolio optimization with real datasets using quantum processors and quantum-inspired tensor networks", Physical Review Research 4 1, 013006 (2022).

[66] Christopher McMahon, Donald McGillivray, Ajit Desai, Francisco Rivadeneyra, Jean-Paul Lam, Thomas Lo, Danica Marsden, and Vladimir Skavysh, "Improving the Efficiency of Payments Systems Using Quantum Computing", Management Science 70 10, 7325 (2024).

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[72] Nikita Guseynov, Xiajie Huang, and Nana Liu, "Quantum framework for simulating linear PDEs with Robin boundary conditions", Quantum Science and Technology 11 1, 015057 (2026).

[73] Antonio Sannia, Rodrigo Martínez-Peña, Miguel C. Soriano, Gian Luca Giorgi, and Roberta Zambrini, "Dissipation as a resource for Quantum Reservoir Computing", Quantum 8, 1291 (2024).

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[94] Francesca Cibrario, Or Samimi Golan, Giacomo Ranieri, Emanuele Dri, Mattia Ippoliti, Ron Cohen, Christian Mattia, Bartolomeo Montrucchio, Amir Naveh, and Davide Corbelletto, 2024 IEEE International Conference on Quantum Computing and Engineering (QCE) 211 (2024) ISBN:979-8-3315-4137-8.

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[102] Nikitas Stamatopoulos, Guglielmo Mazzola, Stefan Woerner, and William J. Zeng, "Towards Quantum Advantage in Financial Market Risk using Quantum Gradient Algorithms", Quantum 6, 770 (2022).

[103] Dong An, Noah Linden, Jin-Peng Liu, Ashley Montanaro, Changpeng Shao, and Jiasu Wang, "Quantum-accelerated multilevel Monte Carlo methods for stochastic differential equations in mathematical finance", Quantum 5, 481 (2021).

[104] Hao Tang, Anurag Pal, Tian‐Yu Wang, Lu‐Feng Qiao, Jun Gao, and Xian‐Min Jin, "Quantum computation for pricing the collateralized debt obligations", Quantum Engineering 3 4(2021).

[105] Sergi Ramos-Calderer, Adrián Pérez-Salinas, Diego García-Martín, Carlos Bravo-Prieto, Jorge Cortada, Jordi Planagumà, and José I. Latorre, "Quantum unary approach to option pricing", Physical Review A 103 3, 032414 (2021).

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[108] Keshav Singh Rawat and Tarun Sharma, "Emerging Paradigm of Quantum Machine Learning: Knowledge Insights and Future Prospects", IEEE Transactions on Artificial Intelligence 7 8, 4252 (2026).

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