Higher-order interpolated lattice schemes for multidimensional option pricing problems

This article presents a new class of higher-order space-time discretization schemes for multidimensional diffusions via lattice systems which involve space interpolation techniques. Through the explanation of the methodology, the author shows that the algorithm can be simply represented by multiplications of sparse matrices. The key idea is to combine the weak approximation approach for stochastic differential equations and some techniques on high-dimensional spaces to break the curse of dimensionality (cubature formulas and sparse grid interpolation techniques). The first objective is to investigate the error estimates derived from short time asymptotics of certain semigroup operators, together with the discussion of numerical stability. As the second objective, several computational experiments for some derivative pricing models are presented in one and three dimensional settings.