Deep Hedging
Deep Hedging
The paper presents a deep reinforcement learning framework for hedging portfolios of derivatives in the presence of market frictions such as transaction costs, market impact, liquidity constraints, and risk limits. The key innovation is to parameterize hedging strategies using deep neural networks, which are trained to minimize a convex risk measure (e.g., entropic risk or optimized certainty equivalent) of the terminal profit and loss. This approach is model-free, meaning it does not require an equivalent martingale measure or computation of Greeks; instead, it relies on a market scenario generator and a loss function. The authors prove that the set of neural network strategies is rich enough to approximate any optimal solution arbitrarily well. Numerical experiments in a Heston model demonstrate that the method outperforms the standard complete-market solution under transaction costs and scales efficiently to high-dimensional settings with multiple hedging instruments. The framework is general and can incorporate various market frictions, making it suitable for practical risk management.
Highlights
- 1Introduces a deep reinforcement learning framework for hedging derivatives under market frictions like transaction costs, liquidity constraints, and risk limits.
- 2Shows that constrained trading strategies parameterized by neural networks can epsilon-approximate any optimal solution.
- 3The method is model-free, scalable to high dimensions, and does not require computing Greeks or an equivalent martingale measure.
- 4Outperforms the standard complete-market solution in a Heston model with transaction costs.
Methods
- MDeep reinforcement learning with neural networks parameterizing hedging strategies.
- MConvex risk measures (e.g., entropic risk measure, optimized certainty equivalents) as objective functions.
- MMini-batch gradient descent (Adam) for training semi-recurrent reinforcement learning problems.
Results
- RNeural network hedging matches the benchmark in a Heston model without transaction costs.
- RProportional transaction costs increase the exponential utility indifference price, as expected.
- RThe method scales to high-dimensional settings (e.g., multiple hedging instruments) with computational cost depending mainly on the number of hedging instruments.
- ROut-of-sample performance demonstrates the effectiveness of the deep hedging approach.
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