Deep learning interpretability for rough volatility

—

Deep learning interpretability for rough volatility

Bo Yuan
Damiano Brigo
Antoine Jacquier
Nicola Pede
Published on 11/28/2024
Equities
FX
Options
Machine learning
Deep learning
Risk management

This paper presents a comprehensive interpretability analysis of deep learning methods applied to rough volatility models, focusing on the rough Heston model. The authors train a feedforward neural network to learn the inverse mapping from implied volatility surfaces (across strikes and maturities) to the model parameters (ρ, V0, κ, θ, ν, H). They generate a synthetic dataset of implied volatilities using Fourier transform pricing methods and then apply several interpretability techniques—including LIME, Gradient*Input, DeepLIFT, LRP, and SHAP—to understand how the neural network makes its predictions.

The key contribution is demonstrating that the neural network's learned mapping is not a black box but can be interpreted in terms of financial intuition. For instance, SHAP analysis shows that the Hurst exponent (H) is the most critical parameter for explaining the at-the-money short-term skew, which aligns with known properties of rough volatility models. The study also finds that other parameters have interpretable effects on different regions of the volatility surface. By providing a framework for interpretability, the paper enhances trust and safety in using neural networks for pricing and calibration in quantitative finance, paving the way for more transparent AI-driven financial models.

Highlights

  • 1Provides the first detailed interpretability analysis of deep learning methods for rough volatility models, specifically the rough Heston model.
  • 2Applies multiple interpretability techniques (LIME, Gradient*Input, DeepLIFT, LRP, SHAP) to understand the neural network's learned mapping from implied volatility surfaces to model parameters.
  • 3Demonstrates that the neural network's learned inverse map aligns with financial intuition, such as the impact of the Hurst exponent on the at-the-money skew.
  • 4Contributes to safer deployment of neural networks in quantitative finance by enhancing transparency and risk monitoring.

Methods

  • M
    Feedforward neural networks (FNN) for learning the inverse map from implied volatilities to rough Heston model parameters.
  • M
    Local interpretability methods: LIME, Gradient*Input, DeepLIFT, Layer-wise Relevance Propagation (LRP).
  • M
    Global interpretability method: Shapley Additive Explanations (SHAP) based on cooperative game theory.
  • M
    Fourier transform methods (Carr-Madan, Lipton, Lewis) for pricing European options under the rough Heston model.

Results

  • R
    The neural network accurately learns the mapping from implied volatility surfaces to rough Heston parameters, achieving low pricing errors.
  • R
    SHAP analysis reveals that the Hurst exponent (H) is the most influential parameter for the at-the-money short-term skew, consistent with financial theory.
  • R
    Local interpretability methods show that the neural network's decisions are consistent with known parameter impacts on the volatility surface.
  • R
    The study validates that the neural network's learned inverse map is interpretable and aligns with mathematical model intuition.
0/5

Analyze Paper

Generate insights from "Deep learning interpretability for rough volatility".

Suggested Actions