TY  - JOUR
N1  - This version is the author accepted manuscript. For information on re-use, please refer to the publisher?s terms and conditions.
IS  - 2
SP  - 625
VL  - 263
A1  - Cui, Y
A1  - del Baño Rollin, S
A1  - Germano, G
JF  - European Journal of Operational Research
SN  - 0377-2217
UR  - http://doi.org/10.1016/j.ejor.2017.05.018
EP  - 638
AV  - public
Y1  - 2017/05/17/
TI  - Full and fast calibration of the Heston stochastic volatility model
KW  - Pricing
KW  -  Heston model
KW  -  Model calibration
KW  -  Optimisation
KW  -  Levenberg?Marquardt method
ID  - discovery1552816
N2  - This paper presents an algorithm for a complete and efficient calibration of the Heston stochastic volatility model. We express the calibration as a nonlinear least-squares problem. We exploit a suitable representation of the Heston characteristic function and modify it to avoid discontinuities caused by branch switchings of complex functions. Using this representation, we obtain the analytical gradient of the price of a vanilla option with respect to the model parameters, which is the key element of all variants of the objective function. The interdependence between the components of the gradient enables an efficient implementation which is around ten times faster than with a numerical gradient. We choose the Levenberg?Marquardt method to calibrate the model and do not observe multiple local minima reported in previous research. Two-dimensional sections show that the objective function is shaped as a narrow valley with a flat bottom. Our method is the fastest calibration of the Heston model developed so far and meets the speed requirement of practical trading.
ER  -