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 or 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 Deep Learning (DDL) 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 DDL 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. DDL 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 DDL. We compare their performance in reducing overfitting and improving the generalisation error. The DDL performance is also compared to the classical DL (without differentiation) one in the case of Feed-Forward Neural Networks. We show that the DDL outperforms the DL.

基于深度学习技术的差分深度学习（DDL）方法应用于Heston模型下的欧式期权定价与标定，DDL技术通过快速训练和准确的定价显著减少了Heston模型的标定计算时间，并表现优于传统深度学习方法。

应用深度学习校准随机波动率模型