Paper: arXiv 2306.11061

Abstract

We propose a neural network-based approach to calibrating stochastic volatility models, which combines the pioneering grid approach by Horvath et al. (2021) with the pointwise two-stage calibration of Bayer et al. (2018) and Liu et al. (2019). Our methodology inherits robustness from the former while not suffering from the need for interpolation/extrapolation techniques, a clear advantage ensured by the pointwise approach. The crucial point to the entire procedure is the generation of implied volatility surfaces on random grids, which one dispenses to the network in the training phase. We support the validity of our calibration technique with several empirical and Monte Carlo experiments for the rough Bergomi and Heston models under a simple but effective parametrization of the forward variance curve. The approach paves the way for valuable applications in financial engineering - for instance, pricing under local stochastic volatility models - and extensions to the fast-growing field of path-dependent volatility models.

Complexity vs Empirical Score

  • Math Complexity: 7.5/10
  • Empirical Rigor: 7.0/10
  • Quadrant: Holy Grail — high math complexity, high empirical rigor

Why this score: The paper employs advanced neural network architectures and stochastic calculus concepts (e.g., rough volatility models, forward variance curves), indicating high mathematical complexity, while it provides extensive Monte Carlo and empirical experiments with specific model calibrations and mentions implementation details like random grids and two-stage training, demonstrating strong empirical rigor.

Research Flowchart

  flowchart TD
  A["Research Goal: Deep Calibration of Stochastic Volatility Models"] --> B["Data: Generate Implied Volatility Surfaces on Random Grids"]
  B --> C["Methodology: Combine Random Grid Approach with Pointwise Two-Stage Calibration"]
  C --> D["Computational Process: Train Neural Network to Learn Calibration Mapping"]
  D --> E["Outcome: Robust & Accurate Calibration for Rough Bergomi & Heston Models"]
  E --> F["Applications: Pricing in LSV Models & Path-Dependent Volatility Models"]