Relationship between deep hedging and delta hedging: leveraging a statistical arbitrage strategy

Abstract

Recently, a new approach, deep hedging has been developed to identify optimal hedging strategies in incomplete markets, to minimize potential losses.
However, the relationship between risk-neutral delta hedging and deep hedging is complicated.
For deep hedging to be useful in practice, we must align with established risk-neutral delta hedging methods.
In this study, we explore the relationship between deep and delta hedging using a statistical arbitrage strategy.
Specifically, we show that hedging that minimizes loss risk combines delta hedging with a statistical arbitrage strategy.
We also discuss how statistical arbitrages can hamper deep hedging.
Finally, we analyze the profit and loss distribution of deep hedging and discuss the risk measures that resist statistical arbitrage.

Keywords: Deep hedging, Risk neutral delta hedging, Risk measures