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Full and fast calibration of the Heston stochastic volatility model

Cui, Yiran, del Baño Rollin, Sebastian and Germano, Guido (2017) Full and fast calibration of the Heston stochastic volatility model. European Journal of Operational Research, 263 (2). pp. 625-638. ISSN 0377-2217

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Identification Number: 10.1016/j.ejor.2017.05.018


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.

Item Type: Article
Official URL:
Additional Information: © 2017 Elsevier B.V.
Divisions: Systemic Risk Centre
Subjects: H Social Sciences > HG Finance
Date Deposited: 14 Aug 2017 10:42
Last Modified: 20 Sep 2021 02:09
Projects: ES/K002309/1
Funders: Economic and Social Research Council

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