Distributional Adversarial Attacks and Training in Deep Hedging

TL;DR

The paper tackles the fragility of deep hedging strategies under distributional shifts by introducing distributional adversarial attacks within a Wasserstein DRO framework and coupling them with adversarial training. It derives tractable attack formulations (WPGD/WBPGD) and demonstrates how to incorporate them into robust hedging via an OCE/DRO objective, validating the approach on Black–Scholes, Heston, and General Affine Diffusion models. Empirical results show that adversarial training improves out-of-sample and out-of-distribution performance, with notable gains in data-scarce regimes and during market stress, and robustness extends to real-market data. The work also discusses limitations, notably the sensitivity to the Wasserstein radius and avenues for extending the framework to other ambiguity sets and attack types, highlighting practical implications for risk management under uncertainty.

Abstract

In this paper, we study the robustness of classical deep hedging strategies under distributional shifts by leveraging the concept of adversarial attacks. We first demonstrate that standard deep hedging models are highly vulnerable to small perturbations in the input distribution, resulting in significant performance degradation. Motivated by this, we propose an adversarial training framework tailored to increase the robustness of deep hedging strategies. Our approach extends pointwise adversarial attacks to the distributional setting and introduces a computationally tractable reformulation of the adversarial optimization problem over a Wasserstein ball. This enables the efficient training of hedging strategies that are resilient to distributional perturbations. Through extensive numerical experiments, we show that adversarially trained deep hedging strategies consistently outperform their classical counterparts in terms of out-of-sample performance and resilience to model misspecification. Additional results indicate that the robust strategies maintain reliable performance on real market data and remain effective during periods of market change. Our findings establish a practical and effective framework for robust deep hedging under realistic market uncertainties.

Figures (5)

• Figure 1: Comparative hedging performance under Heston models. Shaded regions indicate min-max ranges across training partitions.
• Figure 2: Difference in Autocorrelation function (ACF) of perturbed paths for different $\delta$ values and original paths.
• Figure 3: Out-of-sample hedging performance comparison under Black-Scholes dynamics, comparing robust training with clean strategies. Shaded regions indicate min-max ranges across training partitions.
• Figure 4: Out-of-sample hedging performance comparison under Heston model with transaction cost on NetSim, comparing among clean strategies and robust strategies under S-attack and SV-attack.
• Figure 5: Out-of-sample hedging performance comparison under Heston model with transaction cost on NetRec, comparing among clean strategies and robust strategies under S-attack and SV-attack.

Theorems & Definitions (10)

• Theorem 3.3
• Lemma 3.4
• Lemma 4.1
• Corollary 4.2
• proof : Proof of Theorem \ref{['thm:approx_DAA']}
• Theorem C.1: Adapted from bartl2021sensitivitybai2023wasserstein
• proof : Proof of Lemma \ref{['lemma:empirical:V:delta']}
• proof : Proof of Lemma \ref{['lem:budget']}
• Corollary C.2
• proof