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Adversarial Deep Hedging: Learning to Hedge without Price Process Modeling

Masanori HIRANO, Kentaro MINAMI, Kentaro IMAJO

[Preprint] July 25, 2023


Deep hedging is a deep-learning-based framework for derivative hedging in incomplete markets. The advantage of deep hedging lies in its ability to handle various realistic market conditions, such as market frictions, which are challenging to address within the traditional mathematical finance framework. Since deep hedging relies on market simulation, the underlying asset price process model is crucial. However, existing literature on deep hedging often relies on traditional mathematical finance models, e.g., Brownian motion and stochastic volatility models, and discovering effective underlying asset models for deep hedging learning has been a challenge. In this study, we propose a new framework called adversarial deep hedging, inspired by adversarial learning. In this framework, a hedger and a generator, which respectively model the underlying asset process and the underlying asset process, are trained in an adversarial manner. The proposed method enables to learn a robust hedger without explicitly modeling the underlying asset process. Through numerical experiments, we demonstrate that our proposed method achieves competitive performance to models that assume explicit underlying asset processes across various real market data.


Deep Hedging; Price Process; Adversarial Learning; Neural Network; Option; Financial Market;


arXiv:2307.13217 (doi.org/10.48550/arXiv.2307.13217), ssrn.com/abstract=4520273 (doi.org/10.2139/ssrn.4520273)


  title={{Adversarial Deep Hedging: Learning to Hedge without Price Process Modeling}},
  author={Masanori HIRANO and Kentaro MINAMI and Kentaro IMAJO},