In this paper we analyze American style of floating strike Asian call options belonging to the class of financial derivatives whose payoff diagram depends not only on the underlying
asset price but also on the path average of underlying asset prices over some predetermined time
interval. The mathematical model for the option price leads to a free boundary problem for a
parabolic partial differential equation. Applying fixed domain transformation and transformation
of variables we develop an effcient numerical algorithm based on a solution to a non-local parabolic
partial differential equation for the transformed variable representing the synthesized portfolio. For
various types of averaging methods we investigate the dependence of the early exercise boundary
on model parameters.