  This note proposes a method for pricing high-dimensional American options
based on modern methods of multidimensional interpolation. The method allows
using sparse grids and thus mitigates the curse of dimensionality. A framework
of the pricing algorithm and the corresponding interpolation methods are
discussed, and a theorem is demonstrated that suggests that the pricing method
is less vulnerable to the curse of dimensionality. The method is illustrated by
an application to rainbow options and compared to Least Squares Monte Carlo and
other benchmarks.
