Abstract:

Numerical methods of American options are studied. Three numerical schemes arose for solving the optimal exercise boundary of the American option:  the composite trapezoid scheme, composite left rectangular scheme and composite right rectangular scheme. In numerical tests, these three schemes are compared with each other, and finally it is concluded that the composite trapezoid scheme is the best one. Based on numerical schemes of the optimal exercise boundary, a numerical scheme for solving American options is presented by the decomposition of the American option. At last a simulation of an American option is given by this scheme.

Key words: numerical method; American option; optimal exercise boundary; simulation