Paper: arXiv 2502.17757

Authors: Lei Zhao, Lin Cai

Abstract

Deep hedging represents a cutting-edge approach to risk management for financial derivatives by leveraging the power of deep learning. However, existing methods often face challenges related to computational inefficiency, sensitivity to noisy data, and optimization complexity, limiting their practical applicability in dynamic and volatile markets. To address these limitations, we propose Deep Hedging with Linearized-objective Neural Network (DHLNN), a robust and generalizable framework that enhances the training procedure of deep learning models. By integrating a periodic fixed-gradient optimization method with linearized training dynamics, DHLNN stabilizes the training process, accelerates convergence, and improves robustness to noisy financial data. The framework incorporates trajectory-wide optimization and Black-Scholes Delta anchoring, ensuring alignment with established financial theory while maintaining flexibility to adapt to real-world market conditions. Extensive experiments on synthetic and real market data validate the effectiveness of DHLNN, demonstrating its ability to achieve faster convergence, improved stability, and superior hedging performance across diverse market scenarios.

Complexity vs Empirical Score

  • Math Complexity: 6.5/10
  • Empirical Rigor: 7.5/10
  • Quadrant: Holy Grail — high math complexity, high empirical rigor

Why this score: The paper introduces a novel linearized-objective neural network (DHLNN) incorporating Black-Scholes Delta anchoring and periodic fixed-gradient optimization to stabilize deep hedging. It combines a solid theoretical mathematical foundation with extensive empirical validation on both synthetic and real-world market datasets.

Research Flowchart

  flowchart TD
    A[Goal: Robust & Efficient Deep Hedging] --> B[Data Inputs: Synthetic & Real Market Trajectories]
    B --> C[DHLNN Framework Implementation]
    
    subgraph Methodology & Computation
        C --> D[Linearized-Objective NN & Fixed-Gradient Optimization]
        C --> E[Trajectory-Wide Optimization & BS Delta Anchoring]
    end

    D --> F[Evaluations & Stress Testing]
    E --> F
    
    F --> G[Outcomes: Faster Convergence, High Robustness & Superior Hedging]

Cited References (56)

  1. Deep Hedging with Market Impact — → 2402.13326
  2. Deeper Hedging: A New Agent-based Model for Effective Deep Hedging (2023)
  3. Deep reinforcement learning for option replication and hedging (2020)
  4. Deep hedging of derivatives using reinforcement learning (2021) — link
  5. Neural networks for option pricing and hedging: a literature review (2019) — link
  6. Dynamic trading with predictable returns and transaction costs (2013)
  7. Limit order books (2013)
  8. Stochastic calculus for finance II: Continuous-time models (2004)
and 48 more
  1. The volatility surface: A Practitioner’s Guide (2011)
  2. Arbitrage theory in continuous time (2009)
  3. Reinforcement learning in economics and finance (2021)
  4. Deep Reinforcement Learning for Dynamic Stock Option Hedging: A Review (2023)
  5. Stochastic calculus for finance I: the binomial asset pricing model (2005)
  6. Option pricing via breakeven volatility (2023)
  7. Commodity derivatives: markets and applications (2021)
  8. Coherent measures of risk (1999)
  9. Optimization of conditional value-at-risk (2000)
  10. Stochastic finance: an introduction in discrete time (2011)
  11. Portfolio optimization within a Wasserstein ball (2023)
  12. Uncertainty propagation and dynamic robust risk measures — → 2308.12856
  13. Risk Budgeting Allocation for Dynamic Risk Measures — → 2305.11319
  14. Forecasting and trading cryptocurrencies with machine learning under changing market conditions (2021)
  15. Optiver Realized Volatility Prediction (2021) — link
  16. Connecting discrete and continuous path-dependent options (1999)
  17. Options, futures, and other derivatives (2016)
  18. An asymptotic analysis of an optimal hedging model for option pricing with transaction costs (1997)
  19. European option pricing with transaction costs (1993)
  20. Fast finite width neural tangent kernel (2022)
  21. Deep bellman hedging (2022) — link
  22. A neural network approach to understanding implied volatility movements (2020)
  23. A mean field view of the landscape of two-layer neural networks (2018)
  24. Deep hedging of derivatives using reinforcement learning (2020)
  25. Universal statistics of fisher information in deep neural networks: Mean field approach (2019)
  26. Neural tangent kernel: Convergence and generalization in neural networks (2018)
  27. The pricing of options on assets with stochastic volatilities (1987)
  28. An old-new concept of convex risk measures: The optimized certainty equivalent (2007)
  29. Deep portfolio optimization via distributional prediction of residual factors (2021)
  30. Generative Bayesian neural network model for risk-neutral pricing of American index options (2019)
  31. Incorporating Functional Knowledge in Neural Networks. (2009)
  32. A new hybrid parametric and machine learning model with homogeneity hint for European-style index option pricing (2017)
  33. Pricing and hedging derivative securities with neural networks: Bayesian regularization, early stopping, and bagging (2001)
  34. Option pricing and hedging with small transaction costs (2015)
  35. Attention is all you need (2017)
  36. Imagenet classification with deep convolutional neural networks (2012)
  37. Option pricing with transaction costs using a Markov chain approximation (2004)
  38. Indifference pricing: theory and applications (2008)
  39. Utility indifference pricing-an overview (2004)
  40. Optimal replication of contingent claims under transaction costs (1989)
  41. Minimizing transaction costs of option hedging strategies (1996)
  42. A methodology for measuring transaction costs (1991)
  43. The pricing of options and corporate liabilities (1973)
  44. Option pricing and replication with transactions costs (1985)
  45. Neural Ordinary Differential Equations (2018)
  46. On the Equivalence between Neural Network and Support Vector Machine (2021)
  47. No-Transaction Band Network: A Neural Network Architecture for Efficient Deep Hedging (2021) — link
  48. Deep hedging (2019)

3 of 56 cited works are in the corpus; resolved via arXiv source bundles, Semantic Scholar and OpenAlex. Corpus-wide: 2518 linked papers.