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JOURNALS // Zhurnal Vychislitel'noi Matematiki i Matematicheskoi Fiziki // Archive
Zh. Vychisl. Mat. Mat. Fiz., 2019 Volume 59, Number 10, Pages 1815–1820 (Mi zvmmf10975)
This article is cited in 13 papers

Algorithm for determining the volatility function in the Black–Scholes model

V. M. Isakova, S. I. Kabanikhinbcd, A. A. Shananine, M. A. Shishleninbdc, S. Zhangf

a Department of Mathematics and Statistics, Wichita State University, Wichita, Kansas, 67260-0033 USA
b Institute of Computational Mathematics and Mathematical Geophysics of Siberian Branch of Russian Academy of Sciences
c Sobolev Institute of Mathematics, Russian Academy of Sciences, Novosibirsk, 630090 Russia
d Novosibirsk State University, Novosibirsk, 630090 Russia
e Moscow Institute of Physics and Technology, Dolgoprudnyi, Moscow oblast, 141700 Russia
f Beijing, Tianjin University of Finance and Economics, China

Abstract: 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.

Key words: Black–Scholes equation, coefficient inverse problem, optimization, local volatility.

UDC: 519.86

Received: 21.04.2019
Revised: 10.06.2019
Accepted: 10.06.2019

DOI: 10.1134/S0044466919100090


 English version: Computational Mathematics and Mathematical Physics, 2019, 59:10, 1753–1758

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© Steklov Math. Inst. of RAS, 2024