Document Type: Research Paper

**Authors**

Department of Mathematics, Faculty of Science, University of Maragheh, Maragheh, Iran.

**Abstract**

Nonstandard finite difference schemes for the Black-Scholes partial differential equation preserving the positivity property are proposed. Computationally simple schemes are derived by using a nonlocal approximation in the reaction term of the Black-Scholes equation. Unlike the standard methods, the solutions of new proposed schemes are positive and free of the spurious oscillations.

**Keywords**

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