Paper: arXiv 2407.19367

Abstract

This paper proposes a deep delta hedging framework for options, utilizing neural networks to learn the residuals between the hedging function and the implied Black-Scholes delta. This approach leverages the smoother properties of these residuals, enhancing deep learning performance. Utilizing ten years of daily S&P 500 index option data, our empirical analysis demonstrates that learning the residuals, using the mean squared one-step hedging error as the loss function, significantly improves hedging performance over directly learning the hedging function, often by more than 100%. Adding input features when learning the residuals enhances hedging performance more for puts than calls, with market sentiment being less crucial. Furthermore, learning the residuals with three years of data matches the hedging performance of directly learning with ten years of data, proving that our method demands less data.

Complexity vs Empirical Score

  • Math Complexity: 6.5/10
  • Empirical Rigor: 8.0/10
  • Quadrant: Holy Grail — high math complexity, high empirical rigor

Why this score: The paper presents moderately advanced mathematical reasoning around neural network approximation theory and hedging error minimization, while featuring extensive empirical backtesting with ten years of S&P 500 data and quantitative performance comparisons.

Research Flowchart

  flowchart TD
  A["Research Goal:<br>Enhance Delta Hedging with DL"] --> B["Data Input:<br>10Y S&P 500 Option Data"]
  B --> C["Methodology:<br>Deep Learning Framework"]
  C --> D{"Core Strategy?"}
  D --> E["Approach 1:<br>Learn Hedging Function Directly"]
  D --> F["Approach 2:<br>Learn Residuals<br>to Black-Scholes Delta"]
  E --> G["Outcome 1:<br>Baseline Performance"]
  F --> H["Outcome 2:<br>Performance Improved by >100%"]
  F --> I["Outcome 3:<br>Requires 67% less data<br>for equal performance"]

Cited References (45)

  1. Optimal delta hedging for options (2017)
  2. A neural network approach to understanding implied volatility movements (2020)
  3. Learning sequential option hedging models from market data (2021)
  4. Data-driven hedging of stock index options via deep learning (2023)
  5. Hedging with linear regressions and neural networks (2022)
  6. Learning minimum variance discrete hedging directly from the market (2018)
  7. Deep hedging (2019)
  8. Machine learning for quantitative finance: fast derivative pricing, hedging and fitting (2018)
and 37 more
  1. Option hedging using LSTM-RNN: an empirical analysis (2021)
  2. Autoencoder asset pricing models (2021)
  3. Factor Models, Machine Learning, and Asset Pricing (2022)
  4. Machine learning in the Chinese stock market (2022)
  5. Deep learning volatility: a deep neural network perspective on pricing and calibration in (rough) volatility models (2021)
  6. A two-step framework for arbitrage-free prediction of the implied volatility surface (2023)
  7. Option Return Predictability (2022)
  8. Evaluation of Deep Learning Algorithms for Quadratic Hedging (2022)
  9. A factor model for option returns (2022)
  10. An unsupervised deep learning approach to solving partial integro-differential equations (2022)
  11. Solving barrier options under stochastic volatility using deep learning (2022)
  12. An unsupervised deep learning approach to solving partial integro-differential equations (2022)
  13. Solving barrier options under stochastic volatility using deep learning (2022) — link
  14. A Nonparametric Approach to Pricing and Hedging Derivative Securities via Learning Networks (1994)
  15. Pricing and hedging derivative securities with neural networks and a homogeneity hint (2000)
  16. Black–Scholes versus artificial neural networks in pricing FTSE 100 options (2004)
  17. Option pricing with modular neural networks (2009)
  18. Empirical performance of alternative option pricing models (1997)
  19. Implied volatility functions: Empirical tests (1998)
  20. Hedging under SABR model (2006)
  21. Delta-hedging vega risk? (2004)
  22. Regime-dependent smile-adjusted delta hedging (2012)
  23. Approximation by superpositions of a sigmoidal function (1989)
  24. Multilayer feedforward networks are universal approximators (1989)
  25. Universal approximation bounds for superpositions of a sigmoidal function (1993)
  26. Riding on a smile (1994)
  27. Pricing with a smile (1994)
  28. Managing smile risk (2002)
  29. Equal risk pricing of derivatives with deep hedging (2021)
  30. Empirical deep hedging (2023)
  31. Deep Hedging of Derivatives Using Reinforcement Learning (2021)
  32. Dynamic replication and hedging: A reinforcement learning approach (2019)
  33. Deep reinforcement learning for option replication and hedging (2020)
  34. QLBS: Q-Learner in the Black-Scholes (-Merton) Worlds (2020)
  35. The QLBS Q-Learner goes NuQLear: fitted Q iteration, inverse RL, and option portfolios (2019)
  36. Stochastic volatility modeling (2015)
  37. Teaching economics to the machines (2024)

0 of 45 cited works are in the corpus; resolved via arXiv source bundles, Semantic Scholar and OpenAlex. Corpus-wide: 2518 linked papers.