Smart Deep Learning Calibration of the SABR Model

How to structure the topology of a neural net (the hyperparameters optimization) is a recurring problem of crucial importance for both the quality and rapidity of the learning process, which will be then translated onto the final outputs. In this article, the authors investigate a smart two-step procedure that formalizes the application of deep feed-forward neural nets in the problem of the calibration of the SABR option-pricing model. The analysis is performed without the need of manually preparing the network topology, that is instead optimally chosen by means of a Bayesian algorithm. An extensive numerical experiment shows that their approach possesses superior approximation, calibration and retrieval properties when compared to the Hagan's formula and the ZC map.