Deep Gamma Hedging

TL;DR

This paper uses neural networks to learn optimal option hedging strategies with multiple instruments, revealing that gamma hedging primarily addresses model uncertainty rather than transaction costs.

Contribution

It demonstrates that neural networks can replicate Black-Scholes gamma hedging and highlights the role of gamma hedging in managing model uncertainty.

Findings

Neural networks successfully learn gamma hedging strategies.

Gamma hedging is motivated by model uncertainty, not just transaction costs.

The approach works even when underlying dynamics differ from Black-Scholes.

Abstract

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. Our results suggest that the reason gamma hedging is used in practice is to account for model uncertainty rather than to reduce the impact of transaction costs.