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Deep neural network framework based on backward stochastic differential equations for pricing and hedging American options in high dimensions

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  • Yangang Chen
  • Justin W. L. Wan

Abstract

We propose a deep neural network framework for computing prices and deltas of American options in high dimensions. The architecture of the framework is a sequence of neural networks, where each network learns the difference of the price functions between adjacent timesteps. We introduce the least squares residual of the associated backward stochastic differential equation as the loss function. Our proposed framework yields prices and deltas for the entire spacetime, not only at a given point (e.g. t = 0). The computational cost of the proposed approach is quadratic in dimension, which addresses the curse of dimensionality issue that state-of-the-art approaches suffer. Our numerical simulations demonstrate these contributions, and show that the proposed neural network framework outperforms state-of-the-art approaches in high dimensions.

Suggested Citation

  • Yangang Chen & Justin W. L. Wan, 2021. "Deep neural network framework based on backward stochastic differential equations for pricing and hedging American options in high dimensions," Quantitative Finance, Taylor & Francis Journals, vol. 21(1), pages 45-67, January.
    • Handle: RePEc:taf:quantf:v:21:y:2021:i:1:p:45-67
    DOI: 10.1080/14697688.2020.1788219
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    Citations

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    Cited by:

    1. Rushikesh Handal & Kazuki Matoya & Yunzhuo Wang & Masanori Hirano, 2024. "KANOP: A Data-Efficient Option Pricing Model using Kolmogorov-Arnold Networks," Papers 2410.00419, arXiv.org.
    2. Eva Lutkebohmert & Thorsten Schmidt & Julian Sester, 2021. "Robust deep hedging," Papers 2106.10024, arXiv.org, revised Nov 2021.
    3. Salman Bahoo & Marco Cucculelli & Xhoana Goga & Jasmine Mondolo, 2024. "Artificial intelligence in Finance: a comprehensive review through bibliometric and content analysis," SN Business & Economics, Springer, vol. 4(2), pages 1-46, February.
    4. Christian Beck & Lukas Gonon & Arnulf Jentzen, 2024. "Overcoming the curse of dimensionality in the numerical approximation of high-dimensional semilinear elliptic partial differential equations," Partial Differential Equations and Applications, Springer, vol. 5(6), pages 1-47, December.
    5. Jiefei Yang & Guanglian Li, 2024. "Gradient-enhanced sparse Hermite polynomial expansions for pricing and hedging high-dimensional American options," Papers 2405.02570, arXiv.org.
    6. Jiefei Yang & Guanglian Li, 2024. "A deep primal-dual BSDE method for optimal stopping problems," Papers 2409.06937, arXiv.org.
    7. Hao Zhou & Duy-Minh Dang, 2024. "Numerical analysis of American option pricing in a two-asset jump-diffusion model," Papers 2410.04745, arXiv.org, revised Oct 2024.
    8. Ivan Guo & Nicolas Langren'e & Jiahao Wu, 2023. "Simultaneous upper and lower bounds of American-style option prices with hedging via neural networks," Papers 2302.12439, arXiv.org, revised Nov 2024.
    9. Lorenc Kapllani & Long Teng, 2024. "A backward differential deep learning-based algorithm for solving high-dimensional nonlinear backward stochastic differential equations," Papers 2404.08456, arXiv.org.
    10. Yunfei Peng & Pengyu Wei & Wei Wei, 2024. "Deep Penalty Methods: A Class of Deep Learning Algorithms for Solving High Dimensional Optimal Stopping Problems," Papers 2405.11392, arXiv.org.
    11. Andrew Na & Justin Wan, 2023. "Efficient Pricing and Hedging of High Dimensional American Options Using Recurrent Networks," Papers 2301.08232, arXiv.org.
    12. Chinonso Nwankwo & Nneka Umeorah & Tony Ware & Weizhong Dai, 2024. "Deep Learning and American Options via Free Boundary Framework," Computational Economics, Springer;Society for Computational Economics, vol. 64(2), pages 979-1022, August.
    13. Vikranth Lokeshwar Dhandapani & Shashi Jain, 2024. "Optimizing Neural Networks for Bermudan Option Pricing: Convergence Acceleration, Future Exposure Evaluation and Interpolation in Counterparty Credit Risk," Papers 2402.15936, arXiv.org.
    14. Chinonso Nwankwo & Nneka Umeorah & Tony Ware & Weizhong Dai, 2022. "Deep learning and American options via free boundary framework," Papers 2211.11803, arXiv.org, revised Dec 2022.

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