Pascal François, Geneviève Gauthier, Frédéric Godin, Carlos Octavio Pérez Mendoza
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Abstract
Horikawa and Nakagawa (2024) claim that in a complete market admitting statistical arbitrage, the difference between the deep hedging and the replicating portfolio hedging positions is a statistical arbitrage. Deep hedging can thus include an undesirable speculative component. We test whether this remains true in a GARCH-based incomplete 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.
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