Black-Scholes Meet Imitation Learning: Evidence From Deep Hedging in China

Abstract

This paper introduces an imitation learning deep hedging (ILDH) algorithm, which bridges the Black-Scholes-Merton (BSM) model with deep reinforcement learning (DRL) to address the option hedging problem in incomplete real markets. By leveraging imitation learning, the DRL agent optimizes its hedging policy using both freely explored action samples based on real trading data and corresponding action demonstrations derived from the BSM model. These demonstrations serve as data augmentation, enabling the agent to develop a meaningful policy even with a relatively small training data set and enhancing the management of tail risk. Empirical results show that ILDH achieves higher profit, lower risk, and lower cost in the Chinese stock index options market, as compared with other deep hedging algorithms and traditional delta hedging method. This outperformance is robust across call and put options, different transaction cost conditions, and varying levels of risk aversion.