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Mathematical models with time dependent parameters are of great interest infinancial Mathematics because they capture real life scenarios in the financialmarket. In this study, via the Lie group technique, we analyse evolution-typeequations with time dependent parameters and give the general symmetrystructure of these equations. In addition, we illustrate this method by lookingat an example of exotic options called the power options. Our model parametersare time dependent and the option gives a continuous yield dividend atdifferent time intervals. We present new solutions, satisfying the boundaryconditions, to this important problem.

Symmetry structure and solution of evolution-type equations with time dependent parameters in financial Mathematics