Paper: arXiv 2609.02014

Authors: Shuyi Zhang, Frédéric Godin

Abstract

We study deep hedging in the context of dynamics risk measures, where sequential decisions are time-consistent. Whereas the literature in such context mainly considers low-dimensional problems with simple environment dynamics, we tackle the high-dimensional problem of basket option hedging; we show that the approach is feasible and can be used conveniently in the presence of more complex state spaces. We rely on the conditional elicitability of spectral risk measures to represent the optimization objective. We provide insights on how the choice of scoring function impacts the training of the hedging agent. Lastly, the time-consistent hedging strategies are benchmark against deep hedging approaches relying on static risk measures leading to precommitment.

Complexity vs Empirical Score

  • Math Complexity: 8.5/10
  • Empirical Rigor: 7.5/10
  • Quadrant: Holy Grail — high math complexity, high empirical rigor

Why this score: This paper presents a highly mathematical approach to deep hedging, incorporating advanced concepts like elicitable dynamic risk measures and spectral risk measures. It demonstrates strong empirical rigor by applying the method to a high-dimensional basket option hedging problem and benchmarking against static risk measures. The novelty lies in tackling high-dimensional problems with time-consistent deep hedging and providing insights into scoring function choices.

Research Flowchart

  flowchart TD
    A[Research Goal: Time-Consistent Deep Hedging for High-Dimensional Problems] --> B{Key Methodology: Deep Hedging with Dynamic Risk Measures};
    B --> C[Input: Basket Option & Complex State Spaces];
    C --> D{Computational Process: Conditional Elicitability of Spectral Risk Measures};
    D --> E[Computational Process: Training Hedging Agent (Scoring Function Impact)];
    E --> F[Outcome: Feasibility of Time-Consistent Deep Hedging for High-Dim Problems];
    F --> G[Outcome: Insights on Scoring Function Impact & Benchmarking vs. Static Risk Measures];

Cited References (39)

  1. Deep Hedging (2019)
  2. Gamma and Vega Hedging Using Deep Distributional Reinforcement Learning (2023)
  3. Equal Risk Pricing of Derivatives with Deep Hedging (2021)
  4. Deep Equal Risk Pricing of Illiquid Derivatives with Multiple Hedging Instruments (2024)
  5. Conditionally Elicitable Dynamic Risk Measures for Deep Reinforcement Learning (2023)
  6. Reinforcement Learning with Dynamic Convex Risk Measures (2024)
  7. Hedging with Sparse Reward Reinforcement Learning (2025) — link
  8. Deep Reinforcement Learning for Option Replication and Hedging (2020)
and 31 more
  1. Making and Evaluating Point Forecasts (2011)
  2. On the Convergence and Optimality of Policy Gradient for Markov Coherent Risk (2021) — link
  3. Deep Reinforcement Learning for Option Pricing and Hedging under Dynamic Expectile Risk Measures (2023)
  4. Empirical Deep Hedging (2023)
  5. Deep Hedging: Continuous Reinforcement Learning for Hedging of General Portfolios across Multiple Risk Aversions (2022)
  6. Deep Hedging with Market Impact. — → 2402.13326
  7. Deep Reinforcement Learning Algorithms for Option Hedging (2025) — link
  8. Variance-Constrained Actor-Critic Algorithms for Discounted and Average Reward MDPs (2016)
  9. Risk-Averse Dynamic Programming for Markov Decision Processes (2010)
  10. Hedging Beyond the Mean: A Distributional Reinforcement Learning Perspective for Hedging Portfolios with Structured Products (2024) — link
  11. Hedging Barrier Options Using Reinforcement Learning (2024)
  12. On the Global Convergence of Risk-Averse Policy Gradient Methods with Expected Conditional Risk Measures (2023)
  13. QLBS : Q -Learner in the Black–Scholes(-Merton) Worlds (2020) — link
  14. Eliciting Properties of Probability Distributions (2008)
  15. Dynamic Conditional Correlation: A Simple Class of Multivariate Generalized Autoregressive Conditional Heteroskedasticity Models (2002)
  16. Neuronlike Adaptive Elements That Can Solve Difficult Learning Control Problems (1983)
  17. Mastering the Game of Go with Deep Neural Networks and Tree Search (2016)
  18. A General Reinforcement Learning Algorithm That Masters Chess, Shogi, and Go Through Self-Play (2018)
  19. Human -Level Control through Deep Reinforcement Learning (2015)
  20. Enhancing Deep Hedging of Options with Implied Volatility Surface Feedback Information (2024) — link
  21. Deep Hedging with Options Using the Implied Volatility Surface (2025) — link
  22. Variance Adjusted Actor Critic Algorithms (2013) — link
  23. Continuous Control with Deep Reinforcement Learning (2015) — link
  24. Quantile Regression Forests (2006)
  25. Minimizing CVaR in global dynamic hedging with transaction costs (2016)
  26. Robust risk-aware option hedging — → 2303.15216
  27. Robust deep hedging (2022)
  28. Optimization of Conditional Value-at-Risk (2000)
  29. A Closed-Form GARCH Option Valuation Model (2000)
  30. The t Copula and Related Copulas (2005)
  31. Modelling Asymmetric Exchange Rate Dependence (2006)

2 of 39 cited works are in the corpus; resolved via arXiv source bundles, Semantic Scholar and OpenAlex. Corpus-wide: 2518 linked papers.