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

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Listed:
  • Pascal Franc{c}ois
  • Genevi`eve Gauthier
  • Fr'ed'eric Godin
  • Carlos Octavio P'erez Mendoza

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. We observe that the difference between deep hedging and delta hedging can be a statistical arbitrage 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 including a speculative overlay within its hedging strategy.

Suggested Citation

  • Pascal Franc{c}ois & Genevi`eve Gauthier & Fr'ed'eric Godin & Carlos Octavio P'erez Mendoza, 2024. "Is the difference between deep hedging and delta hedging a statistical arbitrage?," Papers 2407.14736, arXiv.org, revised Jul 2024.
    • Handle: RePEc:arx:papers:2407.14736
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    References listed on IDEAS

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