Paper: arXiv 2603.10137

Authors: Manan Poddar

Abstract

Deep hedging trains neural networks to manage derivative risk under market frictions, but produces hedge ratios with no measure of model confidence – a significant barrier to deployment. We introduce uncertainty quantification to the deep hedging framework by training a deep ensemble of five independent 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: the learned strategy outperforms the Black-Scholes delta on approximately 80% of paths when model agreement is high, but on fewer than 20% when disagreement is elevated. We 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 the deployment of machine learning in hedging systems.

Complexity vs Empirical Score

  • Math Complexity: 5.5/10
  • Empirical Rigor: 8.5/10
  • Quadrant: Holy Grail — high math complexity, high empirical rigor

Why this score: The paper makes a novel and practical contribution by introducing deep ensembles for uncertainty quantification in deep hedging. It features strong empirical rigor through extensive market simulations, statistical bootstrap tests, and comparison against established classical benchmarks like the Whalley-Wilmott strategy.

Research Flowchart

  flowchart TD
    A["Research Goal:<br>Quantify model uncertainty in deep hedging under market frictions"] --> B["Inputs:<br>Heston Stochastic Volatility Data & Proportional Transaction Costs"]
    
    B --> C["Deep Ensemble Methodology:<br>Train 5 Independent LSTM Networks"]
    
    C --> D["Uncertainty & Blending Process:<br>1. Measure ensemble disagreement<br>2. Apply CVaR-optimised blending with Black-Scholes delta"]
    
    D --> E["Key Findings & Outcomes:<br>• High agreement = ~80% BS outperformance<br>• Blended strategy improves CVaR by 35-80 bps over BS<br>• Outperforms Whalley-Wilmott by 100-250 bps<br>• Uncertainty driven mainly by option moneyness"]