By: |
Ken-ichi Mitsui (Graduate School of Economics, Osaka University);
Yoshio Tabata (Graduate School of Economics, Osaka University) |
Abstract: |
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. |
Keywords: |
American option, multi-grid methods, wavelet analysis, multiresolution analysis. |
JEL: |
C63 G13 |
Date: |
2005–10 |
URL: |
http://d.repec.org/n?u=RePEc:osk:wpaper:0526&r=ets |