Smart Deep Learning Calibration of the SABR Model

How to structure the topology of a neural net (the hyper-parameters 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 paper we 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 show that our approach, aside from being much faster, possesses superior approximation, calibration and retrieval properties when compared to the Hagan's formula and the ZC Map (Antonov 2013)