Algebraic solutions for pricing American put options under the constant elasticity of variance (CEV) model: Application of the Lie group approach

In this work, the algebraic properties of the American put option under the constant elasticity of variance (CEV) model of financial markets are studied with the implementation of the symmetry approach based on Lie's group theory. The CEV model is described mathematically in terms of the parabolic time–space partial differential equation (PDE) along with the suitable choice of a terminal condition. The classical Lie symmetry analysis is carried out for the governing PDE. Based on the infinitesimal Lie symmetry generators, new classes of group invariant solutions are derived from the mathematical model and the general as well as the specific cases of the CEV model are thoroughly examined. Finally, the results are plotted against the various emergent parameters and their effect are analyzed and discussed.