A fundamental challenge in the numerical solution of multidimensional partial differential equations (PDEs) is the exponential increase of the number of unknowns as the dimensions increase, known as the curse of dimensionality. This creates difficulties in obtaining accurate solutions for even moderate-dimension problems. Researchers have used the sparse grid combination method to reduce the computational workload for multidimensional PDEs. To resolve the unstable order of convergence that arises from the nonsmooth initial conditions, typical of finance problems, researchers applied smoothing (in Fourier space) or, in the case of a Basket option, a clever coordinate transformation that aligns the line of discontinuity with a coordinate axis. We view the transformation through the lens of quantization error, which allows us to determine the minimum order of smoothing required for restoring the order of convergence, and to highlight certain features of smoothing techniques. Additionally, we present numerical results for American options and for options with payoffs that cannot be transformed to align their nonsmoothness regions with a coordinate axis.