Model-Free Deep Hedging with Transaction Costs and Light and Augmented Data Methods

Option pricing theory, in particular the model of Black & Scholes (1973), provides an explicit solution for constructing a perfectly hedged portfolio in continuous time. However, in practice, trading occurs in dis- crete time and is subject to transaction costs, making the direct applica- tion of continuous-time models often suboptimal. Previous studies, such as Buehler et al. (2018), Buehler et al. (2019), and Cao et al. (2019), have shown that deep learning and reinforcement learning can yield superior hedging strategies compared to traditional continuous-time approaches. However, these methods typically rely on a large number of simulated trajectories (on the order of 10^5 to 10^6) for effective training. In this work, we show that it is possible to train a deep hedging neural network using as few as 256 independent trajectories and still outperform both the classical Black & Scholes model and the Leland model in a Ge- ometric Brownian Motion setting. The Leland model is often considered one of the most effective explicit frameworks for incorporating transac- tion costs, yet it is surpassed by our data-efficient neural network when transaction costs are high. Going one step further, we demonstrate that even 256 overlapping sequences can beat the Leland formula when transaction costs are high and that a single trajectory, consisting of 31 or 91 points and augmented with a random drift (our Random Drift Augmentation method) is sufficient to roughly calibrate our neural network. These results highlight the potential for low-data implementations of deep hedging models in practical financial applications