Empirical deep hedging

Existing hedging strategies are typically based on specific financial models: either the strategies are directly based on a given option pricing model or stock price and volatility models are used indirectly by generating synthetic data on which an agent is trained with reinforcement learning. In this paper, we train an agent in a pure data-driven manner. Particularly, we do not need any specifications on volatility or jump dynamics but use large empirical intra-day data from actual stock and option markets. The agent is trained for the hedging of derivative securities using deep reinforcement learning (DRL) with continuous actions. The training data consists of intra-day option price observations on S&P500 index over 6 years, and top of that, we use other data periods for validation and testing. We have two important empirical results. First, a DRL agent trained using synthetic data generated from a calibrated stochastic volatility model outperforms the classic Black-Scholes delta hedging strategy. Second, and more importantly, we find that a DRL agent, which is empirically trained directly using actual intra-day stock and option prices without the prior specification of the underlying volatility or jump processes, has superior performance compared with the use of synthetic data. This implies that DRL can capture the dynamics of S&P500 from the actual intra-day data and to self-learn how to hedge actual options efficiently.