Enhancing Black-Scholes Delta Hedging via Deep Learning

ArXiv ID: 2407.19367 “View on arXiv”

Authors: Unknown

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.

Keywords: Delta Hedging, Deep Learning, Neural Networks, Options Pricing, Residual Learning, Equity Derivatives

Complexity vs Empirical Score

• Math Complexity: 6.5/10
• Empirical Rigor: 8.0/10
• Quadrant: Holy Grail
• Why: 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.

  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"]