Delta Hedging of Derivatives using Deep Reinforcement Learning

Abstract

Building on previous work of Kolm and Ritter (2019) and Cao et al. (2019), this paper explores the novel application of Deep Reinforcement Learning for Delta Hedging of options in an utility based framework where an agent is faced with a trade-off between hedging error and transaction costs while aiming at maximizing the expected profit and loss and minimizing its variance. In the presence of transaction costs we compare the performance of two state-of-the-art Reinforcement Learning algorithms with two simple benchmark strategies widely used in practice. We perform the analysis on synthetic data for different market characteristics, transaction costs, option maturities and hedging frequencies, and find that the agents deliver a strong performance in markets characterized by stochastic volatility and jumps in asset prices, as well as for high transaction costs, high hedging frequency and for options with long maturities. Furthermore, we apply trained algorithms to similar (but not seen before) options and present a way of improving the robustness of the algorithms to different levels of volatility. Finally, we transfer the hedging strategies learned on simulated data to empirical option data on the S&P500 index, and demonstrate that transfer learning is successful: hedge costs encountered by reinforced learning decrease by as much as 30% compared to the Black- Scholes hedging strategy. Our results indicate that the hedging strategies based on Reinforcement Learning outperform the benchmark strategies and are suitable for traders taking real-life hedging decisions, even when the networks are trained on synthetic (but versatile) data.

Keywords: Deep Reinforcement Learning, Derivatives, Delta Hedging, Optimal Control, Deep Q-Networks, Deep Deterministic Policy Gradient, Risk Management, Transaction Costs

JEL Classification: C15, C45, C63, G12