Deep Reinforcement Learning for Option Replication and Hedging

Abstract

The authors propose models for the solution of the fundamental problem of option replication subject to discrete trading, round lotting and nonlinear transaction costs using state-of-the-art methods in deep reinforcement learning (DRL), including deep Q-learning, deep Q-learning with Pop-Art and proximal policy optimization (PPO). Each DRL model is trained to hedge a whole range of strikes and no retraining is needed when the user changes to another strike within the range. The models are general, allowing the user to "plug-in" any option pricing and simulation library, and then training them with no further modifications to hedge arbitrary option portfolios. Through a series of simulations, the authors show that the DRL models learn similar or better strategies as compared to delta hedging. Out of all models, PPO performs the best in terms of P&L, training time and amount of data needed for training.

Keywords: Financial Machine Learning, Hedging, Deep Q-learning, Deep Reinforcement Learning, Deep Neural Networks, Option Replication, Proximal Policy Optimization

JEL Classification: G11, C61