Algebraic properties of evolution partial differential equations modelling prices of commodities

Schwartz (J. Finance 1997; 52:923-973) presented three models for the pricing of a commodity. The simplest was a variation on the Black-Scholes equation. The second allowed for a stochastic convenience yield on the commodity and the third added a stochastic variation in the underlying interest rate. We apply the techniques of Lie group analysis to resolve these equations, discuss their peculiar algebraic properties and indicate the route to the addition of other stochastic influences.