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Full and fast calibration of the Heston stochastic volatility model

Cui, Y; del Baño Rollin, S; Germano, G; (2017) Full and fast calibration of the Heston stochastic volatility model. European Journal of Operational Research , 263 (2) pp. 625-638. 10.1016/j.ejor.2017.05.018. Green open access

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Abstract

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.

Type: Article
Title: Full and fast calibration of the Heston stochastic volatility model
Open access status: An open access version is available from UCL Discovery
DOI: 10.1016/j.ejor.2017.05.018
Publisher version: http://doi.org/10.1016/j.ejor.2017.05.018
Language: English
Additional information: This version is the author accepted manuscript. For information on re-use, please refer to the publisher’s terms and conditions.
Keywords: Pricing, Heston model, Model calibration, Optimisation, Levenberg–Marquardt method
UCL classification: UCL > Provost and Vice Provost Offices
UCL > Provost and Vice Provost Offices > UCL BEAMS
UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Engineering Science
UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Engineering Science > Dept of Computer Science
URI: http://discovery.ucl.ac.uk/id/eprint/1552816
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