IDEAS home Printed from https://ideas.repec.org/a/eee/finlet/v73y2025ics1544612324016192.html
   My bibliography  Save this article

Is the difference between deep hedging and delta hedging a statistical arbitrage?

Author

Listed:
  • François, Pascal
  • Gauthier, Geneviève
  • Godin, Frédéric
  • Mendoza, Carlos Octavio Pérez

Abstract

Horikawa and Nakagawa (2024) claim that in a complete market admitting statistical arbitrage, the difference between the deep hedging and the replicating portfolio hedging positions is a statistical arbitrage. Deep hedging can thus include an undesirable speculative component. We test whether this remains true in a GARCH-based incomplete market dynamics. We observe that the difference between deep hedging and delta hedging is a speculative overlay if the risk measure considered does not put sufficient relative weight on adverse outcomes. Nevertheless, a suitable choice of risk measure can prevent the deep hedging agent from engaging in speculation.

Suggested Citation

  • François, Pascal & Gauthier, Geneviève & Godin, Frédéric & Mendoza, Carlos Octavio Pérez, 2025. "Is the difference between deep hedging and delta hedging a statistical arbitrage?," Finance Research Letters, Elsevier, vol. 73(C).
    • Handle: RePEc:eee:finlet:v:73:y:2025:i:c:s1544612324016192
    DOI: 10.1016/j.frl.2024.106590
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S1544612324016192
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.frl.2024.106590?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. John H. Cochrane & Jesus Saa-Requejo, 2000. "Beyond Arbitrage: Good-Deal Asset Price Bounds in Incomplete Markets," Journal of Political Economy, University of Chicago Press, vol. 108(1), pages 79-119, February.
    2. Saeed Marzban & Erick Delage & Jonathan Yu-Meng Li, 2023. "Deep reinforcement learning for option pricing and hedging under dynamic expectile risk measures," Quantitative Finance, Taylor & Francis Journals, vol. 23(10), pages 1411-1430, October.
    3. Alexandre Carbonneau & Fr'ed'eric Godin, 2021. "Deep Equal Risk Pricing of Financial Derivatives with Multiple Hedging Instruments," Papers 2102.12694, arXiv.org.
    4. Glosten, Lawrence R & Jagannathan, Ravi & Runkle, David E, 1993. "On the Relation between the Expected Value and the Volatility of the Nominal Excess Return on Stocks," Journal of Finance, American Finance Association, vol. 48(5), pages 1779-1801, December.
    5. Alexandre Carbonneau & Frédéric Godin, 2023. "Deep Equal Risk Pricing of Financial Derivatives with Non-Translation Invariant Risk Measures," Risks, MDPI, vol. 11(8), pages 1-27, August.
    6. Hirbod Assa & Keivan Mallahi Karai, 2013. "Hedging, Pareto Optimality, and Good Deals," Journal of Optimization Theory and Applications, Springer, vol. 157(3), pages 900-917, June.
    7. Shota Imaki & Kentaro Imajo & Katsuya Ito & Kentaro Minami & Kei Nakagawa, 2021. "No-Transaction Band Network: A Neural Network Architecture for Efficient Deep Hedging," Papers 2103.01775, arXiv.org.
    8. Pascal Franc{c}ois & Genevi`eve Gauthier & Fr'ed'eric Godin & Carlos Octavio P'erez Mendoza, 2024. "Enhancing Deep Hedging of Options with Implied Volatility Surface Feedback Information," Papers 2407.21138, arXiv.org.
    9. Andrei Neagu & Fr'ed'eric Godin & Clarence Simard & Leila Kosseim, 2024. "Deep Hedging with Market Impact," Papers 2402.13326, arXiv.org, revised Feb 2024.
    10. Oleg Bondarenko, 2003. "Statistical Arbitrage and Securities Prices," The Review of Financial Studies, Society for Financial Studies, vol. 16(3), pages 875-919, July.
    11. Horikawa, Hiroaki & Nakagawa, Kei, 2024. "Relationship between deep hedging and delta hedging: Leveraging a statistical arbitrage strategy," Finance Research Letters, Elsevier, vol. 62(PA).
    12. Reilly Pickard & Yuri Lawryshyn, 2023. "Deep Reinforcement Learning for Dynamic Stock Option Hedging: A Review," Mathematics, MDPI, vol. 11(24), pages 1-19, December.
    13. Ben Hambly & Renyuan Xu & Huining Yang, 2021. "Recent Advances in Reinforcement Learning in Finance," Papers 2112.04553, arXiv.org, revised Feb 2023.
    14. David Wu & Sebastian Jaimungal, 2023. "Robust Risk-Aware Option Hedging," Papers 2303.15216, arXiv.org, revised Dec 2023.
    15. David Wu & Sebastian Jaimungal, 2023. "Robust Risk-Aware Option Hedging," Applied Mathematical Finance, Taylor & Francis Journals, vol. 30(3), pages 153-174, May.
    16. Ben Hambly & Renyuan Xu & Huining Yang, 2023. "Recent advances in reinforcement learning in finance," Mathematical Finance, Wiley Blackwell, vol. 33(3), pages 437-503, July.
    17. Carbonneau, Alexandre, 2021. "Deep hedging of long-term financial derivatives," Insurance: Mathematics and Economics, Elsevier, vol. 99(C), pages 327-340.
    18. Oskari Mikkilä & Juho Kanniainen, 2023. "Empirical deep hedging," Quantitative Finance, Taylor & Francis Journals, vol. 23(1), pages 111-122, January.
    19. El Amine Cherrat & Snehal Raj & Iordanis Kerenidis & Abhishek Shekhar & Ben Wood & Jon Dee & Shouvanik Chakrabarti & Richard Chen & Dylan Herman & Shaohan Hu & Pierre Minssen & Ruslan Shaydulin & Yue , 2023. "Quantum Deep Hedging," Papers 2303.16585, arXiv.org, revised Nov 2023.
    20. Eva Lütkebohmert & Thorsten Schmidt & Julian Sester, 2022. "Robust deep hedging," Quantitative Finance, Taylor & Francis Journals, vol. 22(8), pages 1465-1480, August.
    21. Jay Cao & Jacky Chen & Soroush Farghadani & John Hull & Zissis Poulos & Zeyu Wang & Jun Yuan, 2022. "Gamma and Vega Hedging Using Deep Distributional Reinforcement Learning," Papers 2205.05614, arXiv.org, revised Jan 2023.
    22. Igor Halperin, 2019. "The QLBS Q-Learner goes NuQLear: fitted Q iteration, inverse RL, and option portfolios," Quantitative Finance, Taylor & Francis Journals, vol. 19(9), pages 1543-1553, September.
    23. Blanka Horvath & Josef Teichmann & Zan Zuric, 2021. "Deep Hedging under Rough Volatility," Papers 2102.01962, arXiv.org.
    24. Su, Xiaoshan & Li, Yuhan, 2024. "Robust portfolio selection with subjective risk aversion under dependence uncertainty," Economic Modelling, Elsevier, vol. 132(C).
    25. Blanka Horvath & Josef Teichmann & Zan Zuric, 2021. "Deep Hedging under Rough Volatility," Swiss Finance Institute Research Paper Series 21-88, Swiss Finance Institute.
    26. Alexandre Carbonneau & Frédéric Godin, 2021. "Equal risk pricing of derivatives with deep hedging," Quantitative Finance, Taylor & Francis Journals, vol. 21(4), pages 593-608, April.
    27. El Amine Cherrat & Snehal Raj & Iordanis Kerenidis & Abhishek Shekhar & Ben Wood & Jon Dee & Shouvanik Chakrabarti & Richard Chen & Dylan Herman & Shaohan Hu & Pierre Minssen & Ruslan Shaydulin & Yue , 2023. "Quantum Deep Hedging," Post-Print hal-04263807, HAL.
    28. Blanka Horvath & Josef Teichmann & Žan Žurič, 2021. "Deep Hedging under Rough Volatility," Risks, MDPI, vol. 9(7), pages 1-20, July.
    29. Rockafellar, R. Tyrrell & Uryasev, Stanislav, 2002. "Conditional value-at-risk for general loss distributions," Journal of Banking & Finance, Elsevier, vol. 26(7), pages 1443-1471, July.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Pascal Franc{c}ois & Genevi`eve Gauthier & Fr'ed'eric Godin & Carlos O. P'erez-Mendoza, 2025. "Deep Hedging with Options Using the Implied Volatility Surface," Papers 2504.06208, arXiv.org, revised Apr 2025.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Pascal Franc{c}ois & Genevi`eve Gauthier & Fr'ed'eric Godin & Carlos Octavio P'erez Mendoza, 2024. "Is the difference between deep hedging and delta hedging a statistical arbitrage?," Papers 2407.14736, arXiv.org, revised Oct 2024.
    2. Pascal Franc{c}ois & Genevi`eve Gauthier & Fr'ed'eric Godin & Carlos Octavio P'erez Mendoza, 2024. "Enhancing Deep Hedging of Options with Implied Volatility Surface Feedback Information," Papers 2407.21138, arXiv.org.
    3. Alexandre Carbonneau & Fr'ed'eric Godin, 2021. "Deep equal risk pricing of financial derivatives with non-translation invariant risk measures," Papers 2107.11340, arXiv.org.
    4. Andrei Neagu & Fr'ed'eric Godin & Leila Kosseim, 2025. "Deep Reinforcement Learning Algorithms for Option Hedging," Papers 2504.05521, arXiv.org, revised Apr 2025.
    5. Xianhua Peng & Xiang Zhou & Bo Xiao & Yi Wu, 2024. "A Risk Sensitive Contract-unified Reinforcement Learning Approach for Option Hedging," Papers 2411.09659, arXiv.org.
    6. Horikawa, Hiroaki & Nakagawa, Kei, 2024. "Relationship between deep hedging and delta hedging: Leveraging a statistical arbitrage strategy," Finance Research Letters, Elsevier, vol. 62(PA).
    7. Parisa Davar & Fr'ed'eric Godin & Jose Garrido, 2024. "Catastrophic-risk-aware reinforcement learning with extreme-value-theory-based policy gradients," Papers 2406.15612, arXiv.org, revised Jun 2024.
    8. Konrad Mueller & Amira Akkari & Lukas Gonon & Ben Wood, 2024. "Fast Deep Hedging with Second-Order Optimization," Papers 2410.22568, arXiv.org.
    9. Alexandre Carbonneau & Fr'ed'eric Godin, 2021. "Deep Equal Risk Pricing of Financial Derivatives with Multiple Hedging Instruments," Papers 2102.12694, arXiv.org.
    10. Pascal Franc{c}ois & Genevi`eve Gauthier & Fr'ed'eric Godin & Carlos O. P'erez-Mendoza, 2025. "Deep Hedging with Options Using the Implied Volatility Surface," Papers 2504.06208, arXiv.org, revised Apr 2025.
    11. Chunhui Qiao & Xiangwei Wan, 2024. "Enhancing Black-Scholes Delta Hedging via Deep Learning," Papers 2407.19367, arXiv.org, revised Aug 2024.
    12. Masanori Hirano & Kentaro Minami & Kentaro Imajo, 2023. "Adversarial Deep Hedging: Learning to Hedge without Price Process Modeling," Papers 2307.13217, arXiv.org.
    13. Reilly Pickard & Yuri Lawryshyn, 2023. "Deep Reinforcement Learning for Dynamic Stock Option Hedging: A Review," Mathematics, MDPI, vol. 11(24), pages 1-19, December.
    14. Yiheng Ding & Gangnan Yuan & Dewei Zuo & Ting Gao, 2025. "Hedging with Sparse Reward Reinforcement Learning," Papers 2503.04218, arXiv.org.
    15. Anthony Coache & Sebastian Jaimungal, 2024. "Robust Reinforcement Learning with Dynamic Distortion Risk Measures," Papers 2409.10096, arXiv.org, revised Apr 2025.
    16. Ben Hambly & Renyuan Xu & Huining Yang, 2021. "Recent Advances in Reinforcement Learning in Finance," Papers 2112.04553, arXiv.org, revised Feb 2023.
    17. Carbonneau, Alexandre, 2021. "Deep hedging of long-term financial derivatives," Insurance: Mathematics and Economics, Elsevier, vol. 99(C), pages 327-340.
    18. Ofelia Bonesini & Antoine Jacquier & Alexandre Pannier, 2023. "Rough volatility, path-dependent PDEs and weak rates of convergence," Papers 2304.03042, arXiv.org, revised Jan 2025.
    19. Owen Futter & Blanka Horvath & Magnus Wiese, 2023. "Signature Trading: A Path-Dependent Extension of the Mean-Variance Framework with Exogenous Signals," Papers 2308.15135, arXiv.org, revised Aug 2023.
    20. Beatrice Acciaio & Anastasis Kratsios & Gudmund Pammer, 2022. "Designing Universal Causal Deep Learning Models: The Geometric (Hyper)Transformer," Papers 2201.13094, arXiv.org, revised Mar 2023.

    More about this item

    Keywords

    Deep reinforcement learning; Optimal hedging; Arbitrage;
    All these keywords.

    JEL classification:

    • C45 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: Special Topics - - - Neural Networks and Related Topics
    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis
    • G32 - Financial Economics - - Corporate Finance and Governance - - - Financing Policy; Financial Risk and Risk Management; Capital and Ownership Structure; Value of Firms; Goodwill

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:finlet:v:73:y:2025:i:c:s1544612324016192. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/locate/frl .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.