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

The Heston stochastic volatility model is widely used in financial mathematics for pricing European options. However, calibrating the model remains computationally demanding and is often sensitive to local minima due to its nonlinear structure and high-dimensional parameter space. In this paper, we propose a hybrid deep learning framework designed to improve both the efficiency and accuracy of the calibration process. The approach integrates two supervised feedforward neural networks. The first, referred to as the Price Approximator Network (PAN), approximates the option price surface using strike and moneyness as inputs. The second, the Calibration Correction Network (CCN), refines the Heston model output by correcting systematic pricing errors. Empirical results based on S&P 500 option data indicate that the proposed deep learning approach outperforms traditional calibration methods across several error metrics. In particular, it achieves faster convergence and improved generalization in both in-sample and out-of-sample evaluations. Overall, the proposed framework provides a practical and robust approach for real-time calibration of financial models.