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A Comparison of Reinforcement Learning and Deep Trajectory Based Stochastic Control Agents for Stepwise Mean-Variance Hedging

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  • Ali Fathi
  • Bernhard Hientzsch

Abstract

We consider two data-driven approaches to hedging, Reinforcement Learning and Deep Trajectory-based Stochastic Optimal Control, under a stepwise mean-variance objective. We compare their performance for a European call option in the presence of transaction costs under discrete trading schedules. We do this for a setting where stock prices follow Black-Scholes-Merton dynamics and the "book-keeping" price for the option is given by the Black-Scholes-Merton model with the same parameters. This simulated data setting provides a "sanitized" lab environment with simple enough features where we can conduct a detailed study of strengths, features, issues, and limitations of these two approaches. However, the formulation is model free and could allow any other setting with available book-keeping prices. We consider this study as a first step to develop, test, and validate autonomous hedging agents, and we provide blueprints for such efforts that address various concerns and requirements.

Suggested Citation

  • Ali Fathi & Bernhard Hientzsch, 2023. "A Comparison of Reinforcement Learning and Deep Trajectory Based Stochastic Control Agents for Stepwise Mean-Variance Hedging," Papers 2302.07996, arXiv.org, revised Nov 2023.
    • Handle: RePEc:arx:papers:2302.07996
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    References listed on IDEAS

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    1. Samuel N. Cohen & Derek Snow & Lukasz Szpruch, 2021. "Black-box model risk in finance," Papers 2102.04757, 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. Magnus Wiese & Phillip Murray, 2022. "Risk-Neutral Market Simulation," Papers 2202.13996, arXiv.org.
    4. Jay Cao & Jacky Chen & John Hull & Zissis Poulos, 2021. "Deep Hedging of Derivatives Using Reinforcement Learning," Papers 2103.16409, arXiv.org.
    5. Nicolas Boursin & Carl Remlinger & Joseph Mikael, 2022. "Deep Generators on Commodity Markets Application to Deep Hedging," Risks, MDPI, vol. 11(1), pages 1-18, December.
    6. Narayan Ganesan & Yajie Yu & Bernhard Hientzsch, 2020. "Pricing Barrier Options with DeepBSDEs," Papers 2005.10966, arXiv.org, revised Sep 2024.
    7. A. Max Reppen & H. Mete Soner & Valentin Tissot-Daguette, 2022. "Deep Stochastic Optimization in Finance," Papers 2205.04604, arXiv.org.
    8. Jian Liang & Zhe Xu & Peter Li, 2021. "Deep learning-based least squares forward-backward stochastic differential equation solver for high-dimensional derivative pricing," Quantitative Finance, Taylor & Francis Journals, vol. 21(8), pages 1309-1323, August.
    9. Nicolas Boursin & Carl Remlinger & Joseph Mikael & Carol Anne Hargreaves, 2022. "Deep Generators on Commodity Markets; application to Deep Hedging," Papers 2205.13942, arXiv.org.
    10. Bernhard Hientzsch, 2019. "Introduction to Solving Quant Finance Problems with Time-Stepped FBSDE and Deep Learning," Papers 1911.12231, arXiv.org.
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    Cited by:

    1. Hardik Routray & Bernhard Hientzsch, 2024. "Enforcing asymptotic behavior with DNNs for approximation and regression in finance," Papers 2411.05257, arXiv.org.
    2. Reilly Pickard & Finn Wredenhagen & Julio DeJesus & Mario Schlener & Yuri Lawryshyn, 2024. "Hedging American Put Options with Deep Reinforcement Learning," Papers 2405.06774, arXiv.org.
    3. Reilly Pickard & F. Wredenhagen & Y. Lawryshyn, 2024. "Optimizing Deep Reinforcement Learning for American Put Option Hedging," Papers 2405.08602, arXiv.org.

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