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We present an accurate and efficient numerical method for solving the Black-Scholes equation. The method uses an adaptive grid technique which is based on a far-field boundary position and the Peclet condition. We present the algorithm for the automatic adaptive grid gen- eration: First, we determine a priori suitable far-field boundary location using the mathematical model parameters. Second, generate the uniform fine grid around the non-smooth point of the payoff and a non-uniform grid in the remaining regions. Numerical tests are presented to demon- strate the accuracy and efficiency of the proposed method. Theresults show that the computational time is reduced substantially with the ac- curacy being maintained.

AN ADAPTIVE FINITE DIFFERENCE METHOD USING FAR-FIELD BOUNDARY CONDITIONS FOR THE BLACK-SCHOLES EQUATION