  In the present work, the European option pricing SWIFT method is extended for
Heston model calibration. The computation of the option price gradient is
simplified thanks to the knowledge of the characteristic function in closed
form. The proposed calibration machinery appears to be extremely fast, in
particular for a single expiry and multiples strikes, outperforming the
state-of-the-art method we compare with. Further, the a priori knowledge of
SWIFT parameters makes possible a reliable and practical implementation of the
presented calibration method. A wide set of stress, speed and convergence
numerical experiments is carried out, with deep in-the-money, at-the-money and
deep out-of-the-money options for very short and very long maturities.
