标题： 深度学习增强的Heston模型校准：一个统一的框架 显示英文标题

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

摘要： 赫斯顿随机波动率模型是金融数学中用于定价欧式期权的广泛使用的工具。 然而，由于模型的非线性结构和高维参数空间，其校准仍然计算密集且对局部最小值敏感。 本文介绍了一种基于深度学习的混合框架，该框架提高了校准过程的计算效率和准确性。 所提出的方法集成了两个监督前馈神经网络：价格近似网络（PAN），它根据执行价格和货币性输入近似期权价格表面；以及校准修正网络（CCN），它通过修正系统定价误差来优化赫斯顿模型的输出。 在真实标普500期权数据上的实验结果表明，深度学习方法在多个误差指标上优于传统校准技术，在样本内和样本外设置中均实现了更快的收敛速度和更优的泛化能力。 该框架为实时金融模型校准提供了一个实用且稳健的解决方案。 显示英文摘要

摘要： 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.