Is the Difference between Deep Hedging and Delta Hedging a Statistical Arbitrage?

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