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SWIFT calibration of the Heston model

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  • Eudald Romo
  • Luis Ortiz-Gracia

Abstract

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.

Suggested Citation

  • Eudald Romo & Luis Ortiz-Gracia, 2021. "SWIFT calibration of the Heston model," Papers 2103.01570, arXiv.org.
    • Handle: RePEc:arx:papers:2103.01570
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    References listed on IDEAS

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    1. Cui, Yiran & del Baño Rollin, Sebastian & Germano, Guido, 2017. "Full and fast calibration of the Heston stochastic volatility model," European Journal of Operational Research, Elsevier, vol. 263(2), pages 625-638.
    2. Fang, Fang & Oosterlee, Kees, 2008. "A Novel Pricing Method For European Options Based On Fourier-Cosine Series Expansions," MPRA Paper 9319, University Library of Munich, Germany.
    3. Elisa Alòs & Rafael De Santiago & Josep Vives, 2015. "Calibration Of Stochastic Volatility Models Via Second-Order Approximation: The Heston Case," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 18(06), pages 1-31.
    4. Agnieszka Janek & Tino Kluge & Rafal Weron & Uwe Wystup, 2010. "FX Smile in the Heston Model," Papers 1010.1617, arXiv.org.
    5. Pavel Cizek & Wolfgang Karl Härdle & Rafal Weron, 2005. "Statistical Tools for Finance and Insurance," HSC Books, Hugo Steinhaus Center, Wroclaw University of Science and Technology, number hsbook0501, December.
    6. Heston, Steven L, 1993. "A Closed-Form Solution for Options with Stochastic Volatility with Applications to Bond and Currency Options," The Review of Financial Studies, Society for Financial Studies, vol. 6(2), pages 327-343.
    7. Manfred Gilli & Enrico Schumann, 2010. "Calibrating Option Pricing Models with Heuristics," Working Papers 030, COMISEF.
    8. Manfred Gilli & Enrico Schumann, 2012. "Heuristic optimisation in financial modelling," Annals of Operations Research, Springer, vol. 193(1), pages 129-158, March.
    9. Carlo Cattani, 2008. "Shannon Wavelets Theory," Mathematical Problems in Engineering, Hindawi, vol. 2008, pages 1-24, September.
    10. Paul Glasserman & Kyoung-Kuk Kim, 2011. "Gamma expansion of the Heston stochastic volatility model," Finance and Stochastics, Springer, vol. 15(2), pages 267-296, June.
    11. del Baño Rollin, Sebastian & Ferreiro-Castilla, Albert & Utzet, Frederic, 2010. "On the density of log-spot in the Heston volatility model," Stochastic Processes and their Applications, Elsevier, vol. 120(10), pages 2037-2063, September.
    12. Fernández, J.L. & Ferreiro, A.M. & García-Rodríguez, J.A. & Leitao, A. & López-Salas, J.G. & Vázquez, C., 2013. "Static and dynamic SABR stochastic volatility models: Calibration and option pricing using GPUs," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 94(C), pages 55-75.
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