Uncertainty-Aware Deep Hedging
Uncertainty-Aware Deep Hedging
This paper introduces uncertainty quantification to the deep hedging framework by training a deep ensemble of five LSTM networks under Heston stochastic volatility with proportional transaction costs. The ensemble's disagreement at each time step provides a per-time-step confidence measure that is strongly predictive of hedging performance: when model agreement is high, the learned strategy outperforms the Black-Scholes delta on approximately 80% of paths, but on fewer than 20% when disagreement is elevated. The authors propose a CVaR-optimised blending strategy that combines the ensemble's hedge with the classical Black-Scholes delta, weighted by the level of model uncertainty. The blend improves on the Black-Scholes delta by 35–80 basis points in CVaR across several Heston calibrations, and on the theoretically optimal Whalley-Wilmott strategy by 100–250 basis points, with all improvements statistically significant under paired bootstrap tests.
The analysis reveals that ensemble uncertainty is driven primarily by option moneyness rather than volatility, and that the uncertainty–performance relationship inverts under weak leverage—findings with practical implications for deploying machine learning in hedging systems. The ensemble's advantage over classical hedging arises from transaction cost savings (trading more selectively) rather than from superior price prediction. The choice of risk measure fundamentally determines the optimal blending behaviour: an entropic risk criterion leads to near-complete reliance on the ensemble, while a CVaR criterion favours a classical-dominated blend. The same uncertainty signal supports both strategies, highlighting that uncertainty-aware hedging is a flexible framework accommodating different risk preferences.
Highlights
- 1Introduces uncertainty quantification to deep hedging via deep ensembles, providing per-time-step confidence measures for hedge ratios.
- 2Proposes a CVaR-optimized blending strategy that combines ensemble and Black-Scholes hedges based on model uncertainty, improving tail risk by 35–80 bps over Black-Scholes and 100–250 bps over Whalley-Wilmott.
- 3Demonstrates that ensemble uncertainty is a reliable predictor of hedging performance: high agreement yields ~80% win rate vs. Black-Scholes, while high disagreement yields <20%.
- 4Finds that ensemble uncertainty is driven primarily by option moneyness rather than volatility, and that the uncertainty-performance relationship inverts under weak leverage.
- 5Shows that the ensemble's advantage stems from transaction cost savings (trading selectively) rather than superior price prediction.
Methods
- MDeep ensemble of 5 LSTM networks trained under Heston stochastic volatility with proportional transaction costs.
- MUncertainty-aware blending: hedge ratio = (1-α) * ensemble mean + α * Black-Scholes delta, with α = sigmoid(β0 + β1 * ensemble std dev), optimized for CVaR or entropic risk.
- MPaired bootstrap tests for statistical significance of CVaR improvements.
- MComparison against Black-Scholes delta and Whalley-Wilmott no-transaction-band strategy.
Results
- RCVaR-optimized blend achieves best tail risk: CVaR of -0.0834 vs. -0.0875 (Black-Scholes) and -0.1037 (Whalley-Wilmott) under baseline calibration.
- REnsemble win rate vs. Black-Scholes ranges from 79.8% (lowest uncertainty quintile) to 19.3% (highest uncertainty quintile).
- REnsemble's 14 bps mean P&L advantage over Black-Scholes is entirely due to lower transaction costs (0.06% vs. 0.22% of notional).
- RBlend improves CVaR by 35–80 bps over Black-Scholes and 100–250 bps over Whalley-Wilmott across three Heston calibrations, all statistically significant.
- RUnder low correlation (ρ=-0.3), the uncertainty-performance relationship inverts: ensemble wins on 89% of high-uncertainty paths vs. 13% on low-uncertainty paths.
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