Is the difference between deep hedging and delta hedging a statistical arbitrage?

ArXiv ID: 2407.14736 “View on arXiv”

Authors: Unknown

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.

Keywords: Deep Hedging, Delta Hedging, GARCH Models, Risk Measures, Statistical Arbitrage, Derivatives

Complexity vs Empirical Score

• Math Complexity: 7.5/10
• Empirical Rigor: 8.0/10
• Quadrant: Holy Grail
• Why: 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.

  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