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Uncertainty-Aware Deep Hedging

Manan Poddar

TL;DR

A CVaR-optimised blending strategy is proposed that combines the ensemble's hedge with the classical Black-Scholes delta, weighted by the level of model uncertainty, and reveals that ensemble uncertainty is driven primarily by option moneyness rather than volatility, and that the uncertainty-performance relationship inverts under weak leverage.

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.

Uncertainty-Aware Deep Hedging

TL;DR

A CVaR-optimised blending strategy is proposed that combines the ensemble's hedge with the classical Black-Scholes delta, weighted by the level of model uncertainty, and reveals that ensemble uncertainty is driven primarily by option moneyness rather than volatility, and that the uncertainty-performance relationship inverts under weak leverage.

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.
Paper Structure (36 sections, 9 equations, 4 figures, 12 tables)

This paper contains 36 sections, 9 equations, 4 figures, 12 tables.

Table of Contents

  1. Introduction
  2. Related Work
  3. Deep hedging.
  4. Neural hedging on real data.
  5. Uncertainty quantification in deep learning.
  6. Uncertainty quantification in finance.
  7. Classical hedging under transaction costs.
  8. Methodology
  9. Market Model and Problem Setup
  10. Deep Hedging with Recurrent Networks
  11. Deep Ensembles for Uncertainty Quantification
  12. Classical Baselines
  13. Black--Scholes delta with fixed volatility.
  14. Whalley--Wilmott no-transaction-band strategy.
  15. Uncertainty-Aware Blending
  16. ...and 21 more sections

Figures (4)

  • Figure 1: Ensemble win rate against Black--Scholes delta as a function of path-level uncertainty. Each point represents a rolling window of 500 paths sorted by average ensemble standard deviation. The dashed line marks the 50% break-even threshold.
  • Figure 2: Average ensemble uncertainty as a function of moneyness ($S_t/K$) and time step. Darker colours indicate greater model disagreement. The white region in the lower-left reflects moneyness levels not yet reached by any simulated path at early time steps.
  • Figure 3: Learned blending functions under two optimisation objectives. The entropic risk objective (lower curve) assigns nearly full weight to the ensemble regardless of uncertainty. The CVaR objective (upper curve) assigns majority weight to Black--Scholes delta, with a slight increase at higher uncertainty levels. The dashed line marks equal weighting.
  • Figure 4: CVaR comparison across all four hedging strategies and all three Heston calibrations. Shorter bars (less negative) indicate better tail-risk performance.