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.
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