Lie symmetries, group-invariant solutions and conservation laws of the Vasicek pricing equation of mathematical finance

The one-factor term structure model by Vasicek is analysed from the point of view of Lie symmetry analysis. Its one-parameter Lie point symmetries and corresponding group of adjoint representations are obtained. An optimal system of one-dimensional subalgebras is derived and is then used to obtain symmetry reductions and group-invariant solutions. The group-invariant solutions presented here are new and have not appeared in the literature. Moreover, we derive conservation laws for the Vasicek equation by employing the theorem due to Ibragimov.