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

Pascal Fran\c{c}ois, Genevi\`eve Gauthier, Fr\'ed\'eric Godin and Carlos Octavio P\'erez Mendoza

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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.

Date: 2024-07, Revised 2024-10
New Economics Papers: this item is included in nep-cmp and nep-rmg
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