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Quantum-Inspired Tensor Neural Networks for Option Pricing

Author

Listed:
  • Raj G. Patel
  • Chia-Wei Hsing
  • Serkan Sahin
  • Samuel Palmer
  • Saeed S. Jahromi
  • Shivam Sharma
  • Tomas Dominguez
  • Kris Tziritas
  • Christophe Michel
  • Vincent Porte
  • Mustafa Abid
  • Stephane Aubert
  • Pierre Castellani
  • Samuel Mugel
  • Roman Orus

Abstract

Recent advances in deep learning have enabled us to address the curse of dimensionality (COD) by solving problems in higher dimensions. A subset of such approaches of addressing the COD has led us to solving high-dimensional PDEs. This has resulted in opening doors to solving a variety of real-world problems ranging from mathematical finance to stochastic control for industrial applications. Although feasible, these deep learning methods are still constrained by training time and memory. Tackling these shortcomings, Tensor Neural Networks (TNN) demonstrate that they can provide significant parameter savings while attaining the same accuracy as compared to the classical Dense Neural Network (DNN). In addition, we also show how TNN can be trained faster than DNN for the same accuracy. Besides TNN, we also introduce Tensor Network Initializer (TNN Init), a weight initialization scheme that leads to faster convergence with smaller variance for an equivalent parameter count as compared to a DNN. We benchmark TNN and TNN Init by applying them to solve the parabolic PDE associated with the Heston model, which is widely used in financial pricing theory.

Suggested Citation

  • Raj G. Patel & Chia-Wei Hsing & Serkan Sahin & Samuel Palmer & Saeed S. Jahromi & Shivam Sharma & Tomas Dominguez & Kris Tziritas & Christophe Michel & Vincent Porte & Mustafa Abid & Stephane Aubert &, 2022. "Quantum-Inspired Tensor Neural Networks for Option Pricing," Papers 2212.14076, arXiv.org, revised Mar 2024.
  • Handle: RePEc:arx:papers:2212.14076
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    References listed on IDEAS

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    1. Longstaff, Francis A & Schwartz, Eduardo S, 2001. "Valuing American Options by Simulation: A Simple Least-Squares Approach," The Review of Financial Studies, Society for Financial Studies, vol. 14(1), pages 113-147.
    2. Ricardo Crisóstomo, 2014. "An analisys of the Heston Stochastic Volatility Model: Implementation and Calibration using Matlab," CNMV Working Papers CNMV Working Papers no 58, CNMV- Spanish Securities Markets Commission - Research and Statistics Department.
    3. Darrell Duffie & Jun Pan & Kenneth Singleton, 2000. "Transform Analysis and Asset Pricing for Affine Jump-Diffusions," Econometrica, Econometric Society, vol. 68(6), pages 1343-1376, November.
    4. Yangang Chen & Justin W. L. Wan, 2019. "Deep Neural Network Framework Based on Backward Stochastic Differential Equations for Pricing and Hedging American Options in High Dimensions," Papers 1909.11532, arXiv.org.
    5. Longstaff, Francis A & Schwartz, Eduardo S, 2001. "Valuing American Options by Simulation: A Simple Least-Squares Approach," University of California at Los Angeles, Anderson Graduate School of Management qt43n1k4jb, Anderson Graduate School of Management, UCLA.
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