Paper: arXiv 2407.14736

Abstract

The recent work of Horikawa and Nakagawa (2024) claims that under a complete market admitting statistical arbitrage, the difference between the hedging position provided by deep hedging and that of the replicating portfolio is a statistical arbitrage. This raises concerns as it entails that deep hedging can include a speculative component aimed simply at exploiting the structure of the risk measure guiding the hedging optimisation problem. We test whether such finding remains true in a GARCH-based market model, which is an illustrative case departing from complete market dynamics. We observe that the difference between deep hedging and delta hedging is a speculative overlay if the risk measure considered does not put sufficient relative weight on adverse outcomes. Nevertheless, a suitable choice of risk measure can prevent the deep hedging agent from engaging in speculation.

Complexity vs Empirical Score

  • Math Complexity: 7.5/10
  • Empirical Rigor: 8.0/10
  • Quadrant: Holy Grail — high math complexity, high empirical rigor

Why this score: The paper employs advanced stochastic calculus, deep reinforcement learning with neural network architectures, and formal definitions of statistical arbitrage (CVaR, VaR). Empirically, it features a backtest-ready setup with a GARCH market model, Monte Carlo simulations, 400k training paths, 100k test paths, and includes a GitHub link for code replication.

Research Flowchart

  flowchart TD
  A["Research Goal: Is Deep Hedging<br>vs Delta Hedging<br>a Statistical Arbitrage?"] --> B{"Methodology: GARCH Market Model"}
  B --> C["Data: Simulated Market Paths"]
  C --> D["Process: Optimize Hedging<br>with Risk Measures"]
  D --> E{"Risk Measure Choice"}
  E -- Insufficient Weight<br>on Adverse Outcomes --> F["Outcome: Deep Hedging acts as<br>Speculative Overlay / Stat Arb"]
  E -- Suitable Risk Measure<br>Chosen --> G["Outcome: Speculation Prevented<br>Deep Hedging aligned with Delta"]
  F --> H["Key Finding: Risk measure<br>selection dictates whether<br>deep hedging contains speculation"]
  G --> H

Cited References (37)

  1. Relationship between deep hedging and delta hedging: Leveraging a statistical arbitrage strategy (2024)
  2. Robust risk-aware option hedging — → 2303.15216
  3. Deep hedging: learning to remove the drift under trading frictions with minimal equivalent near-martingale measures (2021) — link
  4. Deep hedging of derivatives using reinforcement learning (2020)
  5. Gamma and vega hedging using deep distributional reinforcement learning (2023)
  6. Deep hedging (2019)
  7. Deep hedging of long-term financial derivatives (2021)
  8. Equal risk pricing of derivatives with deep hedging (2021)
and 29 more
  1. Deep equal risk pricing of financial derivatives with non-translation invariant risk measures (2023)
  2. Approximation capabilities of multilayer feedforward networks (1991)
  3. Empirical deep hedging (2023)
  4. Deep Hedging with Market Impact — → 2402.13326
  5. Recent advances in reinforcement learning in finance (2023)
  6. Deep Reinforcement Learning for Dynamic Stock Option Hedging: A Review (2023)
  7. Quantum deep hedging — → 2303.16585
  8. Deep reinforcement learning for option replication and hedging (2020)
  9. The QLBS Q -Learner goes N u QL ear: F itted Q iteration, inverse RL , and option portfolios (2019)
  10. Robust deep hedging (2022)
  11. Reinforcement learning: An introduction (2018)
  12. Deep hedging: Hedging derivatives under generic market frictions using reinforcement learning (2022)
  13. Deep learning (2016)
  14. Deep equal risk pricing of financial derivatives with multiple hedging instruments (2021) — link
  15. The Pricing of Options and Corporate Liabilities (1973)
  16. Adam: A method for stochastic optimization (2014) — link
  17. Deep reinforcement learning for option pricing and hedging under dynamic expectile risk measures (2023)
  18. Deep hedging under rough volatility (2021)
  19. Deep reinforcement learning for option pricing and hedging under dynamic expectile risk measures (2023) — link
  20. No-Transaction Band Network: A Neural Network Architecture for Efficient Deep Hedging (2021) — link
  21. An empirical analysis of dropout in piecewise linear networks (2013) — link
  22. Understanding the difficulty of training deep feedforward neural networks (2010)
  23. Introduction to Stochastic Calculus Applied to Finance (2011)
  24. On the relation between the expected value and the volatility of the nominal excess return on stocks (1993)
  25. Statistical arbitrage and securities prices (2003)
  26. Hedging, P areto optimality, and good deals (2013)
  27. The GARCH option pricing model (1995)
  28. Beyond arbitrage: Good-deal asset price bounds in incomplete markets (2000)
  29. Enhancing Deep Hedging of Options with Implied Volatility Surface Feedback Information — → 2407.21138

4 of 37 cited works are in the corpus; resolved via arXiv source bundles, Semantic Scholar and OpenAlex. Corpus-wide: 2518 linked papers.