Reinforcement Learning for Option Hedging: Static Implied-Volatility Fit versus Shortfall-Aware Performance

Abstract: We extend the Q-learner in Black-Scholes (QLBS) framework by incorporating risk aversion and trading costs, and propose a novel Replication Learning of Option Pricing (RLOP) approach. Both methods are fully compatible with standard reinforcement learning algorithms and operate under market frictions. Using SPY and XOP option data, we evaluate performance along static and dynamic dimensions. Adaptive-QLBS achieves higher static pricing accuracy in implied volatility space, while RLOP delivers superior dynamic hedging performance by reducing shortfall probability. These results highlight the importance of evaluating option pricing models beyond static fit, emphasizing realized hedging outcomes.