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

arXiv: https://arxiv.org/abs/2510.24074 · HTML: https://mlsanity.com/paper/2510.24074/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 8 of its 35 references that are in the map.
- First posted on arXiv 28 Oct 2025.

## Builds on (most cited first, 8 of 8)

- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [Delving Deep into Rectifiers: Surpassing Human-Level Performance on ImageNet Classification](https://mlsanity.com/paper/1502.01852/) (2015)
- [Deep Hedging](https://mlsanity.com/paper/1802.03042/) (2018)
- [Universal features of price formation in financial markets: perspectives from Deep Learning](https://mlsanity.com/paper/1803.06917/) (2018)
- [Neural networks for option pricing and hedging: a literature review](https://mlsanity.com/paper/1911.05620/) (2019)
- [Deep Learning in Finance](https://mlsanity.com/paper/1602.06561/) (2016)
- [Deep calibration of rough stochastic volatility models](https://mlsanity.com/paper/1810.03399/) (2018)
- [A neural network-based framework for financial model calibration](https://mlsanity.com/paper/1904.10523/) (2019)

## Abstract (arXiv)

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.