A Topological Approach to Parameterizing Deep Hedging Networks
Alok Das, Kiseop Lee
TL;DR
This work tackles the training bottlenecks of deep hedging in incomplete markets by augmenting hedging networks with topological features derived from a 3D Vietoris-Rips embedding of a moving window. The authors show that these features reduce PnL variance and enable smaller batch sizes (e.g., 20) to achieve performance comparable to large-batch training, leading to substantial speedups. Using a Heston-based market model and a cliquet payoff, the approach integrates topological descriptors (L1/L2 norms of birth/death data) into a dual-stream LSTM hedging architecture with a variance-based loss. The results suggest a practical, scalable pathway for data-driven hedging in realistic market settings and highlight topology as a valuable input modality for sequential financial models.
Abstract
Deep hedging uses recurrent neural networks to hedge financial products that cannot be fully hedged in incomplete markets. Previous work in this area focuses on minimizing some measure of quadratic hedging error by calculating pathwise gradients, but doing so requires large batch sizes and can make training effective models in a reasonable amount of time challenging. We show that by adding certain topological features, we can reduce batch sizes substantially and make training these models more practically feasible without greatly compromising hedging performance.