Gamma and Vega Hedging Using Deep Distributional Reinforcement Learning

We consider a trader who is responsible for managing a portfolio of derivatives that evolves stochastically and depends on a single underlying asset. We use reinforcement learning to develop a strategy for bringing options into the portfolio to manage gamma and vega risk. The options are subject to transaction costs. Three different objective functions for managing risk are considered. These involve a mean-variance trade-off, value at risk, and conditional value at risk. We illustrate how the optimal hedging strategy depends on the asset price process, the trader’s objective function, the level of transaction costs, and the maturity of the options used for hedging. We also investigate the robustness of the hedging strategy to the process assumed for the underlying asset and show how the expected profitability of derivatives trading can be evaluated when the strategy is followed