Volatility Surfaces

This chapter explores the application of deep learning to volatility surface calibration across three stochastic volatility models: Heston, SABR and rough Bergomi. The rough Bergomi model, which lacks an analytic form and relies on Monte Carlo simulation, presents a significant computational challenge. Four papers demonstrate the potential of neural networks to accelerate calibration by replacing Monte Carlo simulations. Bayer and Stemper (2018) and Horvath et al. (2019) achieve a 10 4 speedup in calibration for the rough Bergomi model, while McGhee (2018) reports a similar speedup for the SABR model. The papers employ various neural network architectures, including fully connected networks and an inception-based model. Activation functions and regularisation techniques vary across the studies. Synthetic datasets are used for training, with different sampling strategies employed to generate these datasets. The findings highlight the potential of deep learning to enhance the efficiency of volatility surface calibration, with significant implications for financial modelling and practice.