Wavelet based Multi-grid analysis, Wavelet Galerkin method and their Applications to American option: A Survey

This paper surveys the literatures on numerical methods from its origins to present to evaluate American-style claims. An extensive review of numerical meth- ods is provided. In particular, emphases is placed on recent trends and developments in the multi-grid and Galerkin method with the Wavelet basis for American option. Mainly, this paper considers two wavelet based numerical methods. One is that the wavelet basis is used in the restriction and the prolongation in terms of the multi- grid method. The other is the discretization of the components of the Dirichlet problem and the test function in the Galerkin formulation. For the applications of their methods to American option, there are some papers by using the Wavelet Galerkin method with the fixed point iteration method. The multi-grid method without using the Wavelet basis is also used in the American option. It, however, seems that there are not enough studies which are applied to the pricing of Ameri- can options with the wavelet basis.