Lattice Option Pricing By Multidimensional Interpolation

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. The fundamental problem of options theory is the valuation of hybrid, non-linear securities, and options theory is an ingenious but glorified method of interpolation. Emanuel Derman “A guide for the perplexed quant”