numerical method for option pricing model

Analytical solution of generalized black-scholes models are not available,therefore, numerical simulations are of fundamental importance in gaining some useful insights into the solutions. numerical methods based on standard finite differenceapproach, most of the time the essential qualitative properties of the solution are nottransferred to the numerical solution. therefore, this might result in a calamitous erroneous outcome. one way to overcome this disadvantage is to use nonstandard finitedifference methods. in this paper, we propose a non-standard finite difference methodfor solving the generalized black-scholes equation. in constructing the new scheme,we use a nonlocal approximation in the reaction term of the generalized black-scholesequation combined with an implicit time step technique. the new scheme is positivitypreserving, conditionally stable, consistent, and the order of the scheme with respectto the space variable is two. numerical investigations were conducted to validate theseresults. furthermore, the obtained results are more accurate than other existing resultsin the literature