Lattice models are discretization methods that divide the life of a financial option into time steps of equal length and model the underlying asset movement at each time step. A financial option of American or European style can be evaluated conveniently via backward induction using a lattice model. The most common lattice models are the well-known binomial- and trinomial lattice models, although severalkinds of higher order models have also been examined in the literature. In the presentpaper we present an explicit scheme for creating a lattice model of arbitrary order and use the Vandermonde matrix to determine suitable parameters. Some selected models created using this scheme are examined with regard to their suitability for option pricing