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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. Ben Hambly & Renyuan Xu & Huining Yang, 2021. "Recent Advances in Reinforcement Learning in Finance," Papers 2112.04553, arXiv.org, revised Feb 2023.
    2. Hans Buehler & Phillip Murray & Ben Wood, 2022. "Deep Bellman Hedging," Papers 2207.00932, arXiv.org, revised Jan 2023.
    3. Edoardo Vittori & Michele Trapletti & Marcello Restelli, 2020. "Option Hedging with Risk Averse Reinforcement Learning," Papers 2010.12245, arXiv.org.
    4. 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.
    5. Francesco Mandelli & Marco Pinciroli & Michele Trapletti & Edoardo Vittori, 2023. "Reinforcement Learning for Credit Index Option Hedging," Papers 2307.09844, arXiv.org.
    6. 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.
    7. Roberto Daluiso & Marco Pinciroli & Michele Trapletti & Edoardo Vittori, 2023. "CVA Hedging by Risk-Averse Stochastic-Horizon Reinforcement Learning," Papers 2312.14044, arXiv.org.
    8. Zoran Stoiljkovic, 2023. "Applying Reinforcement Learning to Option Pricing and Hedging," Papers 2310.04336, arXiv.org.

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