Abstract
This paper is to investigate the pricing and characterization of the American options of two assets. A common numerical procedure of finding the value of American type options is the finite difference method with Projected Successive Over-Relaxation (Projected SOR). For the options of two assets, the Block Projected SOR method is proposed which is shown to be faster than the usual point iteration. An essentially optimal relaxation parameter ω is found for faster convergence. Comparison is made between the Block SOR method and the lattice method. Also, the early exercise and the hold regions of various American options of two assets are investigated numerically.