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Pricing and hedging American-style options with deep learning

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  • Sebastian Becker
  • Patrick Cheridito
  • Arnulf Jentzen

Abstract

In this paper we introduce a deep learning method for pricing and hedging American-style options. It first computes a candidate optimal stopping policy. From there it derives a lower bound for the price. Then it calculates an upper bound, a point estimate and confidence intervals. Finally, it constructs an approximate dynamic hedging strategy. We test the approach on different specifications of a Bermudan max-call option. In all cases it produces highly accurate prices and dynamic hedging strategies with small replication errors.

Suggested Citation

  • Sebastian Becker & Patrick Cheridito & Arnulf Jentzen, 2019. "Pricing and hedging American-style options with deep learning," Papers 1912.11060, arXiv.org, revised Jul 2020.
    • Handle: RePEc:arx:papers:1912.11060
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    References listed on IDEAS

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    1. Vlad Bally & Gilles Pagès & Jacques Printems, 2005. "A Quantization Tree Method For Pricing And Hedging Multidimensional American Options," Mathematical Finance, Wiley Blackwell, vol. 15(1), pages 119-168, January.
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    Cited by:

    1. Francisco G'omez Casanova & 'Alvaro Leitao & Fernando de Lope Contreras & Carlos V'azquez, 2024. "Deep Joint Learning valuation of Bermudan Swaptions," Papers 2404.11257, arXiv.org.
    2. Lukas Gonon, 2022. "Deep neural network expressivity for optimal stopping problems," Papers 2210.10443, arXiv.org.
    3. Matteo Gambara & Giulia Livieri & Andrea Pallavicini, 2023. "Machine learning methods for American-style path-dependent contracts," Papers 2311.16762, arXiv.org.
    4. Hainaut, Donatien & Akbaraly, Adnane, 2023. "Risk management with Local Least Squares Monte-Carlo," LIDAM Discussion Papers ISBA 2023003, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    5. Calypso Herrera & Florian Krach & Pierre Ruyssen & Josef Teichmann, 2021. "Optimal Stopping via Randomized Neural Networks," Papers 2104.13669, arXiv.org, revised Dec 2023.
    6. John Ery & Loris Michel, 2021. "Solving optimal stopping problems with Deep Q-Learning," Papers 2101.09682, arXiv.org.
    7. Ludovic Gouden`ege & Andrea Molent & Antonino Zanette, 2023. "Backward Hedging for American Options with Transaction Costs," Papers 2305.06805, arXiv.org, revised Jun 2023.
    8. Ivan Guo & Nicolas Langren'e & Jiahao Wu, 2023. "Simultaneous upper and lower bounds of American option prices with hedging via neural networks," Papers 2302.12439, arXiv.org, revised Apr 2024.
    9. Phillip Murray & Ben Wood & Hans Buehler & Magnus Wiese & Mikko S. Pakkanen, 2022. "Deep Hedging: Continuous Reinforcement Learning for Hedging of General Portfolios across Multiple Risk Aversions," Papers 2207.07467, arXiv.org.
    10. Nader Karimi & Erfan Salavati & Hirbod Assa & Hojatollah Adibi, 2023. "Sensitivity Analysis of Optimal Commodity Decision Making with Neural Networks: A Case for COVID-19," Mathematics, MDPI, vol. 11(5), pages 1-15, February.
    11. Riccardo Aiolfi & Nicola Moreni & Marco Bianchetti & Marco Scaringi & Filippo Fogliani, 2021. "Learning Bermudans," Papers 2105.00655, arXiv.org.
    12. Beatriz Salvador & Cornelis W. Oosterlee & Remco van der Meer, 2020. "Financial Option Valuation by Unsupervised Learning with Artificial Neural Networks," Mathematics, MDPI, vol. 9(1), pages 1-20, December.
    13. A. Max Reppen & H. Mete Soner & Valentin Tissot-Daguette, 2022. "Neural Optimal Stopping Boundary," Papers 2205.04595, arXiv.org, revised May 2023.
    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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