Computational Mathematics and Mathematical Physics

, Volume 59, Issue 10, pp 1753–1758 | Cite as

Algorithm for Determining the Volatility Function in the Black–Scholes Model

  • V. M. IsakovEmail author
  • S. I. KabanikhinEmail author
  • A. A. ShananinEmail author
  • M. A. ShishleninEmail author
  • S. ZhangEmail author


An algorithm for reconstructing the volatility function in the modified Black–Scholes model is developed. Results of numerical computations are presented. It is shown that adding information about the prices of similar options with different issue dates makes it possible to improve the accuracy and increase the interval in which the volatility function can be reconstructed.


Black–Scholes equation coefficient inverse problem optimization local volatility 



This work was supported by the Russian Foundation for Basic Research (project nos. 19-01-00694, 17-07-00507, 17-51-150001, 17-51-540004, 16-29-15120, and 16-01-00437) and by NSF (project no. DMS 15-08902).


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Copyright information

© Pleiades Publishing, Ltd. 2019

Authors and Affiliations

  1. 1.Department of Mathematics and Statistics, Wichita State UniversityWichitaUSA
  2. 2.Sobolev Institute of Mathematics, Russian Academy of Sciences, Novosibirsk State UniversityNovosibirskRussia
  3. 3.Moscow Institute of Physics and TechnologyDolgoprudnyiRussia
  4. 4.Tianjin University of Finance and EconomicsBeijingChina

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