Gamma and Vega Hedging Using Deep Distributional Reinforcement Learning

Abstract

We use deep distributional reinforcement learning (RL) to develop a hedging strategy for a trader responsible for derivatives that arrive stochastically and depend on a single underlying asset. The transaction costs associated with trading the underlying asset are usually quite small. The trader therefore normally carries out delta hedging daily, or even more frequently, to ensure that the current portfolio is almost completely insensitive to small movements in the asset's price. Hedging the portfolio's exposure to large asset price movements and volatility changes (gamma and vega hedging) is more expensive because this requires trades in derivatives, for which transaction costs are quite large. Our analysis takes account of these transaction cost differences. It shows how RL can be used to develop a strategy for using options to manage gamma and vega risk with three different objective functions. These objective functions 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 when options are traded, 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.