Abstract
The aim of the present paper is the clarification of the result of A. Paliathanasis, K. Krishnakumar, K.M. Tamizhmani and P.G.L. Leach on the symmetry Lie algebra of the Black–Scholes–Merton equation for European options.
REFERENCES
F. Black and M. Scholes, ‘‘The valuation of option contracts and a test of market efficiency,’’ J. Financ. 27, 399–417 (1972).
F. Black and M. Scholes, ‘‘The pricing of options and corporate liabilities,’’ J. Polit. Econ. 81, 637–659 (1973).
Y. Bozhkov and S. Dimas, ‘‘Group classification of a generalized Black–Scholes–Merton equation,’’ Commun. Nonlin. Sci. Numer. Simul. 19, 2200–2211 (2014). https://doi.org/10.1016/j.cnsns.2013.12.016
R. K. Gazizov and N. H. Ibragimov, ‘‘Lie symmetry analysis of differential equations in finance,’’ Nonlin. Dyn. 17, 387–407 (1998).
R. C. Merton, ‘‘On the pricing of corporate data: The risk structure of interest rates,’’ J. Financ. 29, 449–470 (1974).
A. Paliathanasis, K. Krishnakumar, K. M. Tamizhmani, and P. G. L. Leach, ‘‘Lie symmetry analysis of the Black-Scholes-Merton model for European options with stochastic volatility,’’ Mathematics (Spec. Iss.: Math. Finance) 4 (2), 28 (2016). https://doi.org/10.3390/math4020028.
O. Sinkala, P. Leach, and J. O’Hara, ‘‘Invariance properties of a general bond-pricing equation,’’ J. Diff. Equat. 244, 2820–2835 (2008).
Author information
Authors and Affiliations
Corresponding authors
Additional information
(Submitted by M. A.Malakhaltsev)
Rights and permissions
About this article
Cite this article
Bakirova, L.N., Shurygina, M.A. & Shurygin, V.V. Symmetries of the Black–Scholes–Merton Equation for European Options. Lobachevskii J Math 44, 1256–1263 (2023). https://doi.org/10.1134/S1995080223040042
Received:
Revised:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1134/S1995080223040042