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Deep Gamma Hedging

Author

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  • John Armstrong
  • George Tatlow

Abstract

We train neural networks to learn optimal replication strategies for an option when two replicating instruments are available, namely the underlying and a hedging option. If the price of the hedging option matches that of the Black--Scholes model then we find the network will successfully learn the Black-Scholes gamma hedging strategy, even if the dynamics of the underlying do not match the Black--Scholes model, so long as we choose a loss function that rewards coping with model uncertainty. Our results suggest that the reason gamma hedging is used in practice is to account for model uncertainty rather than to reduce the impact of transaction costs.

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  • John Armstrong & George Tatlow, 2024. "Deep Gamma Hedging," Papers 2409.13567, arXiv.org.
    • Handle: RePEc:arx:papers:2409.13567
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    References listed on IDEAS

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    1. Alexandre Carbonneau, 2020. "Deep Hedging of Long-Term Financial Derivatives," Papers 2007.15128, arXiv.org.
    2. Magnus Wiese & Lianjun Bai & Ben Wood & Hans Buehler, 2019. "Deep Hedging: Learning to Simulate Equity Option Markets," Papers 1911.01700, arXiv.org.
    3. Blanka Horvath & Josef Teichmann & Zan Zuric, 2021. "Deep Hedging under Rough Volatility," Swiss Finance Institute Research Paper Series 21-88, Swiss Finance Institute.
    4. John Armstrong & Andrei Ionescu, 2023. "Gamma Hedging and Rough Paths," Papers 2309.05054, arXiv.org, revised Mar 2024.
    5. Blanka Horvath & Josef Teichmann & Zan Zuric, 2021. "Deep Hedging under Rough Volatility," Papers 2102.01962, arXiv.org.
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