A family of positive nonstandard numerical methods with application to Black-Scholes equation

Nonstandard nite di erence schemes for the Black- Scholes partial di erential 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.