Deep calibration with random grids

Abstract

We propose a neural network-based approach to calibrating stochastic volatility models, which combines the pioneering grid approach by Horvath et al. [Deep learning volatility: A deep neural network perspective on pricing and calibration in (rough) volatility models. Quant. Finance, 2021, 21(1), 11–27]. with the pointwise two-stage calibration of Bayer and Stemper [Deep calibration of rough stochastic volatility models. Working Paper, arXiv:1810.03399, 2018] and Liu et al. [A neural network-based framework for financial model calibration. J. Math. Ind., 2019, 9(1), 1–28]. 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.