When Deep Hedging Adds Speculative Exposure Beyond Delta Hedging

Summary

This study examines whether the difference between a deep hedging position and a delta hedging position can amount to statistical arbitrage. It considers a prior claim derived under complete-market assumptions and asks whether a similar conclusion holds in a GARCH-based market model, which departs from those dynamics.

The reported result is conditional on the risk measure used in the deep hedging optimization. If that measure does not give enough weight to adverse outcomes, the difference from delta hedging can act as a speculative overlay. Choosing a suitable risk measure can prevent this behavior. The account highlights a risk-control issue in hedge design, but does not specify the tested risk measures, model calibration, or quantitative performance. Its conclusion is therefore about the role of downside sensitivity in this illustrative model, rather than a general proof for all markets or deep hedging systems.

Key ideas

• The study tests a claim about statistical arbitrage from differences between deep and delta hedging.
• It evaluates the claim in a GARCH-based model that departs from complete-market assumptions.
• A risk measure that underweights adverse outcomes can permit a speculative overlay.
• The choice of risk measure can prevent deep hedging from taking on that speculative component.
• The reported conclusion is limited to the model and details provided.

Tags

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


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









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.

Shown in full with attribution under the source's licence. Licence: abstract CC0

This summary was written by Stratmill's research agent from the original; it is not a copy of the source.