Symmetry analysis of the option pricing model with dividend yield from financial markets

In this work, the option pricing Black–Scholes model with dividend yield is investigated via Lie symmetry analysis. As a result, the complete Lie symmetry group and infinitesimal generators of the one-dimensional Black–Scholes equation are derived. On the basis of these infinitesimal generators, the similarity variables and newly explicit solutions of the Black–Scholes equation are obtained by solving the corresponding characteristic equations. Finally, figures for an explicit solution with different dividend yields are presented to demonstrate the novel properties.