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The QLBS Q-Learner goes NuQLear: fitted Q iteration, inverse RL, and option portfolios

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  • Igor Halperin

Abstract

The QLBS model is a discrete-time option hedging and pricing model that is based on Dynamic Programming (DP) and Reinforcement Learning (RL). It combines the famous Q-Learning method for RL with the Black–Scholes (–Merton) (BSM) model's idea of reducing the problem of option pricing and hedging to the problem of optimal rebalancing of a dynamic replicating portfolio for the option, which is made of a stock and cash. Here we expand on several NuQLear (Numerical Q-Learning) topics with the QLBS model. First, we investigate the performance of Fitted Q Iteration for an RL (data-driven) solution to the model, and benchmark it versus a DP (model-based) solution, as well as versus the BSM model. Second, we develop an Inverse Reinforcement Learning (IRL) setting for the model, where we only observe prices and actions (re-hedges) taken by a trader, but not rewards. Third, we outline how the QLBS model can be used for pricing portfolios of options, rather than a single option in isolation, thus providing its own, data-driven and model-independent solution to the (in)famous volatility smile problem of the Black–Scholes model.

Suggested Citation

  • 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.
    • Handle: RePEc:taf:quantf:v:19:y:2019:i:9:p:1543-1553
    DOI: 10.1080/14697688.2019.1622302
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    Citations

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    Cited by:

    1. Horikawa, Hiroaki & Nakagawa, Kei, 2024. "Relationship between deep hedging and delta hedging: Leveraging a statistical arbitrage strategy," Finance Research Letters, Elsevier, vol. 62(PA).
    2. Ben Hambly & Renyuan Xu & Huining Yang, 2021. "Recent Advances in Reinforcement Learning in Finance," Papers 2112.04553, arXiv.org, revised Feb 2023.
    3. 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.
    4. 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.
    5. Yuji Shinozaki, 2024. "A Review of New Developments in Finance with Deep Learning: Deep Hedging and Deep Calibration," IMES Discussion Paper Series 24-E-02, Institute for Monetary and Economic Studies, Bank of Japan.
    6. Hans Buehler & Phillip Murray & Ben Wood, 2022. "Deep Bellman Hedging," Papers 2207.00932, arXiv.org, revised Jun 2024.
    7. Edoardo Vittori & Michele Trapletti & Marcello Restelli, 2020. "Option Hedging with Risk Averse Reinforcement Learning," Papers 2010.12245, arXiv.org.
    8. Ahmet Umur Ozsoy & Omur Uu{g}ur, 2023. "The QLBS Model within the presence of feedback loops through the impacts of a large trader," Papers 2311.06790, arXiv.org.
    9. Francesco Mandelli & Marco Pinciroli & Michele Trapletti & Edoardo Vittori, 2023. "Reinforcement Learning for Credit Index Option Hedging," Papers 2307.09844, arXiv.org.
    10. 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.
    11. Chunhui Qiao & Xiangwei Wan, 2024. "Enhancing Black-Scholes Delta Hedging via Deep Learning," Papers 2407.19367, arXiv.org, revised Aug 2024.
    12. Roberto Daluiso & Marco Pinciroli & Michele Trapletti & Edoardo Vittori, 2023. "CVA Hedging by Risk-Averse Stochastic-Horizon Reinforcement Learning," Papers 2312.14044, arXiv.org.
    13. Zoran Stoiljkovic, 2023. "Applying Reinforcement Learning to Option Pricing and Hedging," Papers 2310.04336, arXiv.org.

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