Deep Hedging Under Realistic Market Frictions: A Regime-Conditional Empirical Study of Dynamic Option Hedging on Bitcoin Options

Classical option-hedging methods like Black-Scholes delta assume constant, free rebalancing, which real markets don't allow. Deep hedging trains a neural network to handle these frictions directly, and prior work reports strong results. But those comparisons usually pit deep hedging against a frictionless classical baseline on simulated price data. That's not a fair fight, and it leaves open whether the advantage is real. We test this using five years of actual BTC options data from Deribit (2020-2024), comparing Black-Scholes delta, Leland's cost-adjusted hedge, and the Whalley-Wilmott no-trade band against three deep hedging setups: an LSTM and a feedforward network, each trained with a CVaR loss and, in some runs, a penalty for trading too often. All six strategies face the same 5 basis point transaction cost. On 11,546 test episodes from September 2023 to December 2024, Whalley-Wilmott cuts transaction costs significantly versus hourly rebalancing, saving $1.79 per episode against plain BS delta (95% CI [-2.21, -1.39], p