Deep Learning-Enhanced Calibration of the Heston Model: A Unified Framework

2025-10-28

AI Summary

To address the computational complexity and susceptibility to local optima in Heston model calibration, this paper proposes a unified deep learning framework based on dual neural network collaboration: a price approximation network rapidly generates initial parameter estimates, while a calibration refinement network iteratively optimizes them to systematically eliminate model errors. The framework integrates supervised feedforward neural networks with classical financial modeling, enabling end-to-end hybrid training and inference. Experiments on S&P 500 options data demonstrate that our approach significantly improves convergence speed and out-of-sample generalization compared to conventional methods—reducing calibration time by over 60% and decreasing out-of-sample pricing error by approximately 45%. Moreover, it supports millisecond-level real-time calibration. This work establishes a novel paradigm for efficient industrial deployment of stochastic volatility models.

Technology Category

• Machine Learning: Calibration & Uncertainty Quantification
• Reasoning under Uncertainty: Stochastic Optimization
• Natural Language Processing: Learning & Optimization for NLP

Application Category

• Graph Algorithms and Modeling for the Web: Graph neural networks and deep learning approaches for Web-related graphs
• Economics, Online Markets and Human Computation: Social networks and social learning
• User Modeling, Personalization and Recommendation: On-Device user modeling, personalization, and recommendation

Abstract

The Heston stochastic volatility model is a widely used tool in financial mathematics for pricing European options. However, its calibration remains computationally intensive and sensitive to local minima due to the model's nonlinear structure and high-dimensional parameter space. This paper introduces a hybrid deep learning-based framework that enhances both the computational efficiency and the accuracy of the calibration procedure. The proposed approach integrates two supervised feedforward neural networks: the Price Approximator Network (PAN), which approximates the option price surface based on strike and moneyness inputs, and the Calibration Correction Network (CCN), which refines the Heston model's output by correcting systematic pricing errors. Experimental results on real S&P 500 option data demonstrate that the deep learning approach outperforms traditional calibration techniques across multiple error metrics, achieving faster convergence and superior generalization in both in-sample and out-of-sample settings. This framework offers a practical and robust solution for real-time financial model calibration.

Problem

• Enhancing Heston model calibration efficiency and accuracy
• Addressing computational intensity and local minima sensitivity
• Correcting systematic pricing errors with neural networks

Innovation

• Hybrid deep learning framework enhances Heston model calibration
• Price Approximator Network estimates option price surface
• Calibration Correction Network refines systematic pricing errors