eprintid: 1552816 rev_number: 36 eprint_status: archive userid: 608 dir: disk0/01/55/28/16 datestamp: 2017-04-22 21:57:19 lastmod: 2021-10-16 22:08:25 status_changed: 2017-08-15 10:50:50 type: article metadata_visibility: show creators_name: Cui, Y creators_name: del Baño Rollin, S creators_name: Germano, G title: Full and fast calibration of the Heston stochastic volatility model ispublished: pub divisions: UCL divisions: B04 divisions: C05 divisions: F48 keywords: Pricing, Heston model, Model calibration, Optimisation, Levenberg–Marquardt method note: This version is the author accepted manuscript. For information on re-use, please refer to the publisher’s terms and conditions. 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. date: 2017-05-17 date_type: published official_url: http://doi.org/10.1016/j.ejor.2017.05.018 oa_status: green full_text_type: other language: eng primo: open primo_central: open_green article_type_text: Journal Article verified: verified_manual elements_id: 1280000 doi: 10.1016/j.ejor.2017.05.018 lyricists_name: Germano, Guido lyricists_id: GGERM33 actors_name: Germano, Guido actors_name: Stacey, Thomas actors_id: GGERM33 actors_id: TSSTA20 actors_role: owner actors_role: impersonator full_text_status: public publication: European Journal of Operational Research volume: 263 number: 2 pagerange: 625-638 issn: 0377-2217 citation: 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 <https://doi.org/10.1016/j.ejor.2017.05.018>. Green open access document_url: https://discovery.ucl.ac.uk/id/eprint/1552816/1/Germano_full%20and%20fast%20calibration_Heston_EurJOperRes_263_625_2017_accepted.pdf document_url: https://discovery.ucl.ac.uk/id/eprint/1552816/6/Germano_full%20and%20fast%20calibration_Heston_EurJOperRes_263_625_2017_suppl.zip