  We consider the one-factor model of commodities for which the parameters of
the model depend upon the stock price or on the time. For that model we study
the existence of group-invariant transformations. When the parameters are
constant, the one-factor model is maximally symmetric. That also holds for the
time-dependent problem. However, in the case for which the parameters depend
upon the stock price (space) the one-factor model looses the group invariants.
For specific functional forms of the parameters the model admits other possible
Lie algebras. In each case we determine the conditions which the parameters
should satisfy in order for the equation to admit Lie point symmetries. Some
applications are given and we show which should be the precise relation amongst
the parameters of the model in order for the equation to be maximally
symmetric. Finally we discuss some modifications of the initial conditions in
the case of the space-dependent model. We do that by using geometric
techniques.
