  We present a numerical approach for solving the free boundary problem for the
Black-Scholes equation for pricing American style of floating strike Asian
options. A fixed domain transformation of the free boundary problem into a
parabolic equation defined on a fixed spatial domain is performed. As a result
a nonlinear time-dependent term is involved in the resulting equation. Two new
numerical algorithms are proposed. In the first algorithm a predictor-corrector
scheme is used. The second one is based on the Newton method. Computational
experiments, confirming the accuracy of the algorithms are presented and
discussed.
