The importance of positive coefficients in numerical schemes is frequently emphasized in the finance literature. This paper outlines the conditions under which finite volume/element methods applied to two factor option pricing partial differerntial equations give rise to discretizations with positive coefficients. Numerical experiments indicate that constructing a mesh which satisfies positive coefficient conditions may be not only unnecessary, but in some cases even detrimental. As well, it is shown that schemes with negative coefficients due to the discretization of the diffusion term satisfy approximate local maximum and minimum conditions as the mesh spacing approaches zero. This finding is of significance since, for arbitrary diffusion tensors, it may not be possible to construct a positive coefficient discretization for a given set of nodes. In addition, it is shown that several lattice methods are equivalent to finite element schemes with a particular choice of node location.
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