VaR Estimation with Quantum Computing Noise Correction Using Neural Networks
In this paper, we present the development of a quantum computing method for calculating the value at risk (<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>V</mi><mi>a</mi><mi...
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| Jezik: | English |
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MDPI AG
2023-10-01
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| Serija: | Mathematics |
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| Online pristup: | https://www.mdpi.com/2227-7390/11/20/4355 |
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| author | Luis de Pedro Raúl París Murillo Jorge E. López de Vergara Sergio López-Buedo Francisco J. Gómez-Arribas |
| author_facet | Luis de Pedro Raúl París Murillo Jorge E. López de Vergara Sergio López-Buedo Francisco J. Gómez-Arribas |
| author_sort | Luis de Pedro |
| collection | DOAJ |
| description | In this paper, we present the development of a quantum computing method for calculating the value at risk (<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>V</mi><mi>a</mi><mi>R</mi></mrow></semantics></math></inline-formula>) for a portfolio of assets managed by a finance institution. We extend the conventional Monte Carlo algorithm to calculate the <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>V</mi><mi>a</mi><mi>R</mi></mrow></semantics></math></inline-formula> of an arbitrary number of assets by employing random variable algebra and Taylor series approximation. The resulting algorithm is suitable to be executed in real quantum computers. However, the noise affecting current quantum computers renders them almost useless for the task. We present a methodology to mitigate the noise impact by using neural networks to compensate for the noise effects. The system combines the output from a real quantum computer with the neural network processing. The feedback is used to fine tune the quantum circuits. The results show that this approach is useful for estimating the <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>V</mi><mi>a</mi><mi>R</mi></mrow></semantics></math></inline-formula> in finance institutions, particularly when dealing with a large number of assets. We demonstrate the validity of the proposed method with up to 139 assets. The accuracy of the method is also proven. We achieved an error of less than <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mn>1</mn><mo>%</mo></mrow></semantics></math></inline-formula> in the empirical measurements with respect to the parametric model. |
| first_indexed | 2024-03-10T21:04:58Z |
| format | Article |
| id | doaj.art-abca54455690439f8765fc1270df8339 |
| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-03-10T21:04:58Z |
| publishDate | 2023-10-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj.art-abca54455690439f8765fc1270df83392023-11-19T17:14:50ZengMDPI AGMathematics2227-73902023-10-011120435510.3390/math11204355VaR Estimation with Quantum Computing Noise Correction Using Neural NetworksLuis de Pedro0Raúl París Murillo1Jorge E. López de Vergara2Sergio López-Buedo3Francisco J. Gómez-Arribas4Escuela Politécnica Superior, Universidad Autónoma de Madrid, 28049 Madrid, SpainEscuela Politécnica Superior, Universidad Autónoma de Madrid, 28049 Madrid, SpainEscuela Politécnica Superior, Universidad Autónoma de Madrid, 28049 Madrid, SpainEscuela Politécnica Superior, Universidad Autónoma de Madrid, 28049 Madrid, SpainEscuela Politécnica Superior, Universidad Autónoma de Madrid, 28049 Madrid, SpainIn this paper, we present the development of a quantum computing method for calculating the value at risk (<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>V</mi><mi>a</mi><mi>R</mi></mrow></semantics></math></inline-formula>) for a portfolio of assets managed by a finance institution. We extend the conventional Monte Carlo algorithm to calculate the <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>V</mi><mi>a</mi><mi>R</mi></mrow></semantics></math></inline-formula> of an arbitrary number of assets by employing random variable algebra and Taylor series approximation. The resulting algorithm is suitable to be executed in real quantum computers. However, the noise affecting current quantum computers renders them almost useless for the task. We present a methodology to mitigate the noise impact by using neural networks to compensate for the noise effects. The system combines the output from a real quantum computer with the neural network processing. The feedback is used to fine tune the quantum circuits. The results show that this approach is useful for estimating the <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>V</mi><mi>a</mi><mi>R</mi></mrow></semantics></math></inline-formula> in finance institutions, particularly when dealing with a large number of assets. We demonstrate the validity of the proposed method with up to 139 assets. The accuracy of the method is also proven. We achieved an error of less than <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mn>1</mn><mo>%</mo></mrow></semantics></math></inline-formula> in the empirical measurements with respect to the parametric model.https://www.mdpi.com/2227-7390/11/20/4355neural networkqubitquantum computingMonte Carlovalue at risk (<i>VaR</i>) |
| spellingShingle | Luis de Pedro Raúl París Murillo Jorge E. López de Vergara Sergio López-Buedo Francisco J. Gómez-Arribas VaR Estimation with Quantum Computing Noise Correction Using Neural Networks Mathematics neural network qubit quantum computing Monte Carlo value at risk (<i>VaR</i>) |
| title | VaR Estimation with Quantum Computing Noise Correction Using Neural Networks |
| title_full | VaR Estimation with Quantum Computing Noise Correction Using Neural Networks |
| title_fullStr | VaR Estimation with Quantum Computing Noise Correction Using Neural Networks |
| title_full_unstemmed | VaR Estimation with Quantum Computing Noise Correction Using Neural Networks |
| title_short | VaR Estimation with Quantum Computing Noise Correction Using Neural Networks |
| title_sort | var estimation with quantum computing noise correction using neural networks |
| topic | neural network qubit quantum computing Monte Carlo value at risk (<i>VaR</i>) |
| url | https://www.mdpi.com/2227-7390/11/20/4355 |
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