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We consider the one-factor model of commodities for which the parameters ofthe model depend upon the stock price or on the time. For that model we studythe existence of group-invariant transformations. When the parameters areconstant, the one-factor model is maximally symmetric. That also holds for thetime-dependent problem. However, in the case for which the parameters dependupon the stock price (space) the one-factor model looses the group invariants.For specific functional forms of the parameters the model admits other possibleLie algebras. In each case we determine the conditions which the parametersshould satisfy in order for the equation to admit Lie point symmetries. Someapplications are given and we show which should be the precise relation amongstthe parameters of the model in order for the equation to be maximallysymmetric. Finally we discuss some modifications of the initial conditions inthe case of the space-dependent model. We do that by using geometrictechniques.

The algebraic properties of the space- and time-dependent one-factor model of commodities