Is the Difference between Deep Hedging and Delta Hedging a Statistical Arbitrage?
15 Pages Posted: 31 Jul 2024 Last revised: 21 Oct 2024
Date Written: July 30, 2024
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.
Keywords: Deep reinforcement learning, optimal hedging, arbitrage
JEL Classification: C45, C61, G32
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