Paper: arXiv 2510.16938

Authors: Alok Das, Kiseop Lee

Abstract

Deep hedging uses recurrent neural networks to hedge financial products that cannot be fully hedged in incomplete markets. Previous work in this area focuses on minimizing some measure of quadratic hedging error by calculating pathwise gradients, but doing so requires large batch sizes and can make training effective models in a reasonable amount of time challenging. We show that by adding certain topological features, we can reduce batch sizes substantially and make training these models more practically feasible without greatly compromising hedging performance.

Complexity vs Empirical Score

  • Math Complexity: 5.5/10
  • Empirical Rigor: 6.5/10
  • Quadrant: Holy Grail — high math complexity, high empirical rigor

Why this score: The paper introduces an innovative application of Topological Data Analysis (TDA) to improve training stability and efficiency in Deep Hedging for path-dependent options (Cliquet). The empirical backtesting on simulated Heston paths demonstrates convincing variance reduction and training efficiency gains, though it relies purely on synthetic data rather than historical market observations.

Research Flowchart

  flowchart TD
    A["Research Goal: Accelerate Deep Hedging<br/>Training in Incomplete Markets"] --> B["Input: Financial Derivatives Data<br/>& Asset Paths"]
    B --> C["Integrate Topological Features<br/>into Recurrent Neural Network"]
    C --> D["Optimize Model via Pathwise Gradients<br/>with Reduced Batch Sizes"]
    D --> E["Outcome: Faster, Practically Feasible Training<br/>with Maintained Hedging Performance"]

Cited References (16)

  1. Fast Deep Hedging with Second-Order Optimization — → 2410.22568
  2. Identifying Extreme Events in the Stock Market: A Topological Data Analysis (2024) — link
  3. An Introduction to Topological Data Analysis: Fundamental and Practical Aspects for Data Scientists (2021) — link
  4. Deep Hedging (2018) — link
  5. Deep Hedging with Options Using the Implied Volatility Surface — → 2504.06208
  6. Reinforcement Learning and Deep Stochastic Optimal Control for Final Quadratic Hedging — → 2401.08600
  7. A Closed-Form Solution for Options with Stochastic Volatility with Applications to Bond and Currency Options (1993) — link
  8. Deep Hedging of Long-Term Financial Derivatives (2020) — link
and 8 more
  1. Empirical Deep Hedging (2022) — link
  2. Deep Hedging of Derivatives Using Reinforcement Learning (2021) — link
  3. No-Transaction Band Network: A Neural Network Architecture for Efficient Deep Hedging (2023) — link
  4. Deep Hedging with Market Impact — → 2402.13326
  5. Deep Hedging Under Non-Convexity: Limitations and a Case for AlphaZero (2025) — link
  6. Deep Hedging Bermudan Swaptions (2024) — link
  7. Hedging Barrier Options Using Reinforcement Learning (2023) — link
  8. Topological Persistence and Simplification (2002)

4 of 16 cited works are in the corpus; resolved via arXiv source bundles, Semantic Scholar and OpenAlex. Corpus-wide: 2518 linked papers.