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Pricing and Hedging American-Style Options with Deep Learning

Author

Listed:
  • Sebastian Becker

    (RiskLab, ETH Zurich, 8092 Zurich, Switzerland)

  • Patrick Cheridito

    (RiskLab, ETH Zurich, 8092 Zurich, Switzerland)

  • Arnulf Jentzen

    (Faculty of Mathematics and Computer Science, University of Münster, 48149 Münster, Germany)

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, 2020. "Pricing and Hedging American-Style Options with Deep Learning," JRFM, MDPI, vol. 13(7), pages 1-12, July.
  • Handle: RePEc:gam:jjrfmx:v:13:y:2020:i:7:p:158-:d:386598
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    References listed on IDEAS

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    Citations

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    Cited by:

    1. John Ery & Loris Michel, 2021. "Solving optimal stopping problems with Deep Q-Learning," Papers 2101.09682, arXiv.org.
    2. 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.
    3. Lukas Gonon, 2022. "Deep neural network expressivity for optimal stopping problems," Papers 2210.10443, 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. Ludovic Gouden`ege & Andrea Molent & Antonino Zanette, 2023. "Backward Hedging for American Options with Transaction Costs," Papers 2305.06805, arXiv.org, revised Jun 2023.
    6. 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.
    7. A. Max Reppen & H. Mete Soner & Valentin Tissot-Daguette, 2022. "Neural Optimal Stopping Boundary," Papers 2205.04595, arXiv.org, revised May 2023.
    8. Calypso Herrera & Florian Krach & Pierre Ruyssen & Josef Teichmann, 2021. "Optimal Stopping via Randomized Neural Networks," Papers 2104.13669, arXiv.org, revised Dec 2023.
    9. 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.
    10. Riccardo Aiolfi & Nicola Moreni & Marco Bianchetti & Marco Scaringi & Filippo Fogliani, 2021. "Learning Bermudans," Papers 2105.00655, arXiv.org.
    11. 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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