Pricing Multiasset Derivatives by Variational Quantum Algorithms
Pricing a multiasset derivative is an important problem in financial engineering, both theoretically and practically. Although it is suitable to numerically solve partial differential equations to calculate the prices of certain types of derivatives, the computational complexity increases exponentia...
| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
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IEEE
2023-01-01
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| Series: | IEEE Transactions on Quantum Engineering |
| Subjects: | |
| Online Access: | https://ieeexplore.ieee.org/document/10112619/ |
| _version_ | 1797322567012319232 |
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| author | Kenji Kubo Koichi Miyamoto Kosuke Mitarai Keisuke Fujii |
| author_facet | Kenji Kubo Koichi Miyamoto Kosuke Mitarai Keisuke Fujii |
| author_sort | Kenji Kubo |
| collection | DOAJ |
| description | Pricing a multiasset derivative is an important problem in financial engineering, both theoretically and practically. Although it is suitable to numerically solve partial differential equations to calculate the prices of certain types of derivatives, the computational complexity increases exponentially as the number of underlying assets increases in some classical methods, such as the finite difference method. Therefore, there are efforts to reduce the computational complexity by using quantum computation. However, when solving with naive quantum algorithms, the target derivative price is embedded in the amplitude of one basis of the quantum state, and so an exponential complexity is required to obtain the solution. To avoid the bottleneck, our previous study utilizes the fact that the present price of a derivative can be obtained by its discounted expected value at any future point in time and shows that the quantum algorithm can reduce the complexity. In this article, to make the algorithm feasible to run on a small quantum computer, we use variational quantum simulation to solve the Black–Scholes equation and compute the derivative price from the inner product between the solution and a probability distribution. This avoids the measurement bottleneck of the naive approach and would provide quantum speedup even in noisy quantum computers. We also conduct numerical experiments to validate our method. Our method will be an important breakthrough in derivative pricing using small-scale quantum computers. |
| first_indexed | 2024-03-08T05:16:11Z |
| format | Article |
| id | doaj.art-8972e5d256924eb9a45afcbba507ff66 |
| institution | Directory Open Access Journal |
| issn | 2689-1808 |
| language | English |
| last_indexed | 2024-03-08T05:16:11Z |
| publishDate | 2023-01-01 |
| publisher | IEEE |
| record_format | Article |
| series | IEEE Transactions on Quantum Engineering |
| spelling | doaj.art-8972e5d256924eb9a45afcbba507ff662024-02-07T00:04:02ZengIEEEIEEE Transactions on Quantum Engineering2689-18082023-01-01411710.1109/TQE.2023.326952510112619Pricing Multiasset Derivatives by Variational Quantum AlgorithmsKenji Kubo0https://orcid.org/0000-0002-9059-7159Koichi Miyamoto1Kosuke Mitarai2Keisuke Fujii3Mercari R4D, Mercari, Inc., Tokyo, JapanCenter for Quantum Information and Quantum Biology, Osaka University, Osaka, JapanGraduate School of Engineering Science, Osaka University, Osaka, JapanGraduate School of Engineering Science, Osaka University, Osaka, JapanPricing a multiasset derivative is an important problem in financial engineering, both theoretically and practically. Although it is suitable to numerically solve partial differential equations to calculate the prices of certain types of derivatives, the computational complexity increases exponentially as the number of underlying assets increases in some classical methods, such as the finite difference method. Therefore, there are efforts to reduce the computational complexity by using quantum computation. However, when solving with naive quantum algorithms, the target derivative price is embedded in the amplitude of one basis of the quantum state, and so an exponential complexity is required to obtain the solution. To avoid the bottleneck, our previous study utilizes the fact that the present price of a derivative can be obtained by its discounted expected value at any future point in time and shows that the quantum algorithm can reduce the complexity. In this article, to make the algorithm feasible to run on a small quantum computer, we use variational quantum simulation to solve the Black–Scholes equation and compute the derivative price from the inner product between the solution and a probability distribution. This avoids the measurement bottleneck of the naive approach and would provide quantum speedup even in noisy quantum computers. We also conduct numerical experiments to validate our method. Our method will be an important breakthrough in derivative pricing using small-scale quantum computers.https://ieeexplore.ieee.org/document/10112619/Derivative pricingfinite difference methods (FDMs)variational quantum computing |
| spellingShingle | Kenji Kubo Koichi Miyamoto Kosuke Mitarai Keisuke Fujii Pricing Multiasset Derivatives by Variational Quantum Algorithms IEEE Transactions on Quantum Engineering Derivative pricing finite difference methods (FDMs) variational quantum computing |
| title | Pricing Multiasset Derivatives by Variational Quantum Algorithms |
| title_full | Pricing Multiasset Derivatives by Variational Quantum Algorithms |
| title_fullStr | Pricing Multiasset Derivatives by Variational Quantum Algorithms |
| title_full_unstemmed | Pricing Multiasset Derivatives by Variational Quantum Algorithms |
| title_short | Pricing Multiasset Derivatives by Variational Quantum Algorithms |
| title_sort | pricing multiasset derivatives by variational quantum algorithms |
| topic | Derivative pricing finite difference methods (FDMs) variational quantum computing |
| url | https://ieeexplore.ieee.org/document/10112619/ |
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