  With some transformations, we convert the problem of option pricing under
state-dependent volatility into an initial value problem of the Fokker-Planck
equation with a certain potential. By using the Lie symmetry analysis and
similarity reduction method, we are able to reduce the dimensions of the
partial differential equation and find some of its particular solutions of the
equation. A few case studies demonstrate that our new method can be used to
produce analytical option pricing formulas for certain volatility functions.
