Calibrating the Heston model with deep differential networks

ArXiv ID: 2407.15536 “View on arXiv”

Authors: Unknown

Abstract

We propose a gradient-based deep learning framework to calibrate the Heston option pricing model (Heston, 1993). Our neural network, henceforth deep differential network (DDN), learns both the Heston pricing formula for plain-vanilla options and the partial derivatives with respect to the model parameters. The price sensitivities estimated by the DDN are not subject to the numerical issues that can be encountered in computing the gradient of the Heston pricing function. Thus, our network is an excellent pricing engine for fast gradient-based calibrations. Extensive tests on selected equity markets show that the DDN significantly outperforms non-differential feedforward neural networks in terms of calibration accuracy. In addition, it dramatically reduces the computational time with respect to global optimizers that do not use gradient information.

Keywords: Deep Differential Network (DDN), Heston Model, Calibration, Option Pricing, Sensitivities, Equity Derivatives (Options)

Complexity vs Empirical Score

• Math Complexity: 8.0/10
• Empirical Rigor: 7.0/10
• Quadrant: Holy Grail
• Why: The paper employs advanced mathematics including stochastic calculus, Fourier inversion for Heston pricing, and partial derivative analysis, while providing extensive empirical tests on equity markets with performance metrics and computational time reductions.

  flowchart TD
    A["Research Goal<br>Accurate & Fast Heston Calibration"] --> B["Data: Market Option Data"]
    B --> C["Method: Deep Differential Network (DDN)"]
    C --> D["Compute: Price & Sensitivities"]
    D --> E["Optimization: Gradient-Based"]
    E --> F["Outcome: Calibrated Parameters"]
    F --> G["Key Findings<br>Better Accuracy & Faster Speed"]