MOHAMMAD MEHDIZADEH KHALSARAEI - Department of Mathematics, Faculty of Science, University of Maragheh,Maragheh, Iran.
NASHMIL OSMANI - Department of Mathematics, Faculty of Science, University of Maragheh,Maragheh, Iran

Nonstandard finite difference schemes for the BlackScholes partial differential equation preserving the positivity property are proposed. Computationally simple schemes are derived byusing a nonlocal approximation in the reaction term of the BlackScholes equation. Unlike the standard methods, the solutions ofnew proposed schemes are positive and free of the spurious oscillations.

Black-Scholes equation, Option pricing, Finite differencescheme, Positivity-preserving