  In this paper, we consider the numerical pricing of financial derivatives
using Radial Basis Function generated Finite Differences in space. Such
discretization methods have the advantage of not requiring Cartesian grids.
Instead, the nodes can be placed with higher density in areas where there is a
need for higher accuracy. Still, the discretization matrix is fairly sparse. As
a model problem, we consider the pricing of European options in 2D. Since such
options have a discontinuity in the first derivative of the payoff function
which prohibits high order convergence, we smooth this function using an
established technique for Cartesian grids. Numerical experiments show that we
acquire a fourth order scheme in space, both for the uniform and the nonuniform
node layouts that we use. The high order method with the nonuniform node layout
achieves very high accuracy with relatively few nodes. This renders the
potential for solving pricing problems in higher spatial dimensions since the
computational memory and time demand become much smaller with this method
compared to standard techniques.
