  We propose a neural network-based approach to calibrating stochastic
volatility models, which combines the pioneering grid approach by Horvath et
al. (2021) with the pointwise two-stage calibration of Bayer et al. (2018) and
Liu et al. (2019). Our methodology inherits robustness from the former while
not suffering from the need for interpolation/extrapolation techniques, a clear
advantage ensured by the pointwise approach. The crucial point to the entire
procedure is the generation of implied volatility surfaces on random grids,
which one dispenses to the network in the training phase. We support the
validity of our calibration technique with several empirical and Monte Carlo
experiments for the rough Bergomi and Heston models under a simple but
effective parametrization of the forward variance curve. The approach paves the
way for valuable applications in financial engineering - for instance, pricing
under local stochastic volatility models - and extensions to the fast-growing
field of path-dependent volatility models.
