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Deep Hedging: Learning to Remove the Drift under Trading Frictions with Minimal Equivalent Near-Martingale Measures

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Listed:
  • Hans Buehler
  • Phillip Murray
  • Mikko S. Pakkanen
  • Ben Wood

Abstract

We present a machine learning approach for finding minimal equivalent martingale measures for markets simulators of tradable instruments, e.g. for a spot price and options written on the same underlying. We extend our results to markets with frictions, in which case we find "near-martingale measures" under which the prices of hedging instruments are martingales within their bid/ask spread. By removing the drift, we are then able to learn using Deep Hedging a "clean" hedge for an exotic payoff which is not polluted by the trading strategy trying to make money from statistical arbitrage opportunities. We correspondingly highlight the robustness of this hedge vs estimation error of the original market simulator. We discuss applications to two market simulators.

Suggested Citation

  • Hans Buehler & Phillip Murray & Mikko S. Pakkanen & Ben Wood, 2021. "Deep Hedging: Learning to Remove the Drift under Trading Frictions with Minimal Equivalent Near-Martingale Measures," Papers 2111.07844, arXiv.org, revised Jan 2022.
    • Handle: RePEc:arx:papers:2111.07844
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    File URL: http://arxiv.org/pdf/2111.07844
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    References listed on IDEAS

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    1. Magnus Wiese & Lianjun Bai & Ben Wood & Hans Buehler, 2019. "Deep Hedging: Learning to Simulate Equity Option Markets," Papers 1911.01700, arXiv.org.
    2. Marco Frittelli, 2000. "The Minimal Entropy Martingale Measure and the Valuation Problem in Incomplete Markets," Mathematical Finance, Wiley Blackwell, vol. 10(1), pages 39-52, January.
    3. Aharon Ben‐Tal & Marc Teboulle, 2007. "An Old‐New Concept Of Convex Risk Measures: The Optimized Certainty Equivalent," Mathematical Finance, Wiley Blackwell, vol. 17(3), pages 449-476, July.
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    Cited by:

    1. Magnus Wiese & Ben Wood & Alexandre Pachoud & Ralf Korn & Hans Buehler & Phillip Murray & Lianjun Bai, 2021. "Multi-Asset Spot and Option Market Simulation," Papers 2112.06823, arXiv.org.
    2. 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.
    3. Magnus Wiese & Phillip Murray & Ralf Korn, 2023. "Sig-Splines: universal approximation and convex calibration of time series generative models," Papers 2307.09767, arXiv.org.
    4. Magnus Wiese & Phillip Murray, 2022. "Risk-Neutral Market Simulation," Papers 2202.13996, arXiv.org.

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