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Robust deep hedging

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  • Eva Lütkebohmert
  • Thorsten Schmidt
  • Julian Sester

Abstract

We study pricing and hedging under parameter uncertainty for a class of Markov processes which we call generalized affine processes and which includes the Black–Scholes model as well as the constant elasticity of variance (CEV) model as special cases. Based on a general dynamic programming principle, we are able to link the associated nonlinear expectation to a variational form of the Kolmogorov equation which opens the door for fast numerical pricing in the robust framework. The main novelty of the paper is that we propose a deep hedging approach which efficiently solves the hedging problem under parameter uncertainty. We numerically evaluate this method on simulated and real data and show that the robust deep hedging outperforms existing hedging approaches in highly volatile periods.

Suggested Citation

  • Eva Lütkebohmert & Thorsten Schmidt & Julian Sester, 2022. "Robust deep hedging," Quantitative Finance, Taylor & Francis Journals, vol. 22(8), pages 1465-1480, August.
    • Handle: RePEc:taf:quantf:v:22:y:2022:i:8:p:1465-1480
    DOI: 10.1080/14697688.2022.2056073
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    • Eva Lutkebohmert & Thorsten Schmidt & Julian Sester, 2021. "Robust deep hedging," Papers 2106.10024, arXiv.org, revised Nov 2021.

    References listed on IDEAS

    as
    1. Eva Lütkebohmert & Julian Sester, 2019. "Tightening robust price bounds for exotic derivatives," Quantitative Finance, Taylor & Francis Journals, vol. 19(11), pages 1797-1815, November.
    2. Sandrine Gumbel & Thorsten Schmidt, 2020. "Machine learning for multiple yield curve markets: fast calibration in the Gaussian affine framework," Papers 2004.07736, arXiv.org, revised Apr 2020.
    3. Tolulope Fadina & Ariel Neufeld & Thorsten Schmidt, 2018. "Affine processes under parameter uncertainty," Papers 1806.02912, arXiv.org, revised Mar 2019.
    4. Sandrine Gümbel & Thorsten Schmidt, 2020. "Machine Learning for Multiple Yield Curve Markets: Fast Calibration in the Gaussian Affine Framework," Risks, MDPI, vol. 8(2), pages 1-18, May.
    5. Christa Cuchiero & Wahid Khosrawi & Josef Teichmann, 2020. "A generative adversarial network approach to calibration of local stochastic volatility models," Papers 2005.02505, arXiv.org, revised Sep 2020.
    6. B. Acciaio & M. Beiglböck & F. Penkner & W. Schachermayer, 2016. "A Model-Free Version Of The Fundamental Theorem Of Asset Pricing And The Super-Replication Theorem," Mathematical Finance, Wiley Blackwell, vol. 26(2), pages 233-251, April.
    7. Christa Cuchiero & Wahid Khosrawi & Josef Teichmann, 2020. "A Generative Adversarial Network Approach to Calibration of Local Stochastic Volatility Models," Risks, MDPI, vol. 8(4), pages 1-31, September.
    8. Bruno Bouchard & Marcel Nutz, 2013. "Arbitrage and duality in nondominated discrete-time models," Papers 1305.6008, arXiv.org, revised Mar 2015.
    9. 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.
    10. 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.
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    Citations

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    Cited by:

    1. 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.
    2. Ariel Neufeld & Julian Sester & Daiying Yin, 2022. "Detecting data-driven robust statistical arbitrage strategies with deep neural networks," Papers 2203.03179, arXiv.org, revised Feb 2024.
    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. Carl Remlinger & Joseph Mikael & Romuald Elie, 2022. "Robust Operator Learning to Solve PDE," Working Papers hal-03599726, HAL.
    5. Ariel Neufeld & Julian Sester & Mario Šikić, 2023. "Markov decision processes under model uncertainty," Mathematical Finance, Wiley Blackwell, vol. 33(3), pages 618-665, July.
    6. 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).

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