Stochastic volatility models, where the volatility is a stochastic process, can capture most of the essential stylized facts of implied volatility surfaces and give more realistic dynamics of the volatility smile/skew. However, they come with the significant issue that they take too long to calibrate. Alternative calibration methods based on Deep Learning (DL) techniques have been recently used to build fast and accurate solutions to the calibration problem. Huge and Savine developed a Differential Machine Learning (DML) approach, where Machine Learning models are trained on samples of not only features and labels but also differentials of labels to features. The present work aims to apply the DML technique to price vanilla European options (i.e. the calibration instruments), more specifically, puts when the underlying asset follows a Heston model and then calibrate the model on the trained network. DML allows for fast training and accurate pricing. The trained neural network dramatically reduces Heston calibration's computation time. In this work, we also introduce different regularisation techniques, and we apply them notably in the case of the DML. We compare their performance in reducing overfitting and improving the generalisation error. The DML performance is also compared to the classical DL (without differentiation) one in the case of Feed-Forward Neural Networks. We show that the DML outperforms the DL. The complete code for our experiments is provided in the GitHub repository: https://github.com/asridi/DML-Calibration-Heston-Model

翻译：随机波动率模型将波动率视为随机过程，能够捕捉隐含波动率曲面的主要典型特征，并给出波动率微笑/偏斜更真实的动态特性。然而，这类模型存在校准时间过长这一显著问题。基于深度学习技术的替代校准方法近年来已被用于构建快速且精确的校准解决方案。Huge与Savine开发了一种微分机器学习方法，该方法在训练机器学习模型时不仅使用特征与标签样本，还引入了标签对特征的微分信息。本研究旨在将微分机器学习技术应用于欧式香草期权（即校准工具）定价，具体而言是标的资产服从Heston模型时的看跌期权定价，并在训练好的网络上完成模型校准。微分机器学习实现了快速训练与精确定价，训练好的神经网络大幅缩短了Heston模型的校准计算时间。本研究还引入了多种正则化技术，并将其重点应用于微分机器学习场景。我们比较了这些正则化技术在降低过拟合与改善泛化误差方面的性能。在前馈神经网络架构下，本研究还将微分机器学习的性能与经典深度学习（不含微分）进行了对比，结果表明微分机器学习优于经典深度学习。本实验的完整代码已托管于GitHub仓库：https://github.com/asridi/DML-Calibration-Heston-Model