Deep Gamma Hedging

We train neural networks to learn optimal replication strategies for an option when two replicating instruments are available, namely the underlying and a hedging option. If the price of the hedging option matches that of the Black–Scholes model then we find the network will successfully learn the Black–Scholes gamma hedging strategy, even if the dynamics of the underlying do not match the Black–Scholes model, so long as we choose a loss function that rewards coping with model uncertainty. While transaction costs have been cited as a motivation for reducing gamma exposure, our results indicate that model uncertainty provides an even stronger incentive.