  Mathematical models with time dependent parameters are of great interest in
financial Mathematics because they capture real life scenarios in the financial
market. In this study, via the Lie group technique, we analyse evolution-type
equations with time dependent parameters and give the general symmetry
structure of these equations. In addition, we illustrate this method by looking
at an example of exotic options called the power options. Our model parameters
are time dependent and the option gives a continuous yield dividend at
different time intervals. We present new solutions, satisfying the boundary
conditions, to this important problem.
