This paper addresses the computational bottleneck of calibrating rough stochastic volatility models, such as the rough Bergomi model, by proposing a two-step deep learning approach. In the first step, a neural network is trained to approximate the pricing map from model parameters to implied volatilities (or option prices) using synthetic data generated by Monte Carlo simulations. The second step uses traditional optimization algorithms, specifically Levenberg-Marquardt, on the neural network surrogate to calibrate model parameters to market data. This separation leverages the speed of neural network evaluations and automatic differentiation for fast Jacobian computation, while maintaining interpretability and compatibility with existing risk management frameworks.

The authors compare different neural network architectures, including pointwise and grid-based approaches, and find that a remarkably small network (3 layers, 30 neurons) suffices for grid-based calibration, enabling deployment on standard CPUs without GPUs. Numerical experiments demonstrate that the method achieves high accuracy for the rough Bergomi model, which is notoriously difficult to calibrate due to the high cost of Monte Carlo pricing. Additionally, the fast pricing surrogate facilitates Bayesian analysis, allowing uncertainty quantification of calibrated parameters. The approach is model-agnostic and can be applied to other stochastic volatility models, with simpler architectures sufficient for classical models like Heston or SABR. Overall, the paper provides a practical and efficient solution for real-time calibration of complex financial models.