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In this paper, we present an implicit finite difference method for thenumerical solution of the Black-Scholes model of American put options withoutdividend payments. We combine the proposed numerical method by using a frontfixing approach where the option price and the early exercise boundary arecomputed simultaneously. Consistency and stability properties of the method arestudied. We choose to improve the accuracy of the computed solution via a meshrefinement based on Richardson's extrapolation. Comparisons with some proposedmethods for the American options problem are carried out to validate theobtained numerical results and to show the efficiency of the proposed numericalmethods. Finally, by \textit{a posteriori} error estimator, we find a suitablecomputational grid requiring that the computed solution verifies a prefixedtolerance.

A Front Fixing Implicit Finite Difference Method for the American Put Options Model