Abstract: The Lie group analysis of differential equation was developed by Sophus Lie in the end of the 19th century. The theory was further improved during the 20th century, thanks to new progress in the field of mathematical physics. The theory of Lie Groups provide an algorithmic procedure to find all the symmetries of ordinary and partial differential equation. The knowledge of symmetries, permits to write the differential equation in a simpler form, and sometimes to find immediately a possible solution. Nowadays more papers use this method in applications to different models in financial mathematics.