Generalized Finite Integration Method with space–time decomposition technique for solving high dimensional option pricing models

In this paper, the recently developed Generalized Finite Integration Method (GFIM) is further combined with the technique of domain decomposition to solve multiple assets option pricing problems. By taking the time as a temporal variable incorporated with the spatial variables, we apply the space–time decomposition technique to divide the time interval into disjoint union of sub-intervals. The approximate solution at each sub-domain can then be obtained by using the GFIM iteratively. The advantage of this GFIM with space–time decomposition technique will be demonstrated by the numerical examples of solving free-boundary American option and two-assets exchange options pricing problems.