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

Abstract

In this study, we explore the links between deep hedging 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. The numerical experiments in a simple Black–Scholes world also verify these results. Moreover, it is known that the existence of statistical arbitrages can hamper proper learning of deep hedging. For this problem, the obtained relationship and analysis of the profit and loss (PnL) distribution of deep hedging provide us with insight into risk measures that are resistant to statistical arbitrages. We conclude that the use of these robust risk measures allows us to ignore the estimation of drift terms in asset price processes.