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 difference approach, most of the time
the essential qualitative properties of the solution are not transferred to the numerical solution.
Therefore, this might result in a calamitous erroneous outcome. One way to overcome this
disadvantage is to use nonstandard finite difference methods. In this paper, we propose a
non-standard finite difference method for solving the generalized Black-Scholes equation. In
constructing the new scheme, we use a nonlocal approximation in the reaction term of the
generalized Black-Scholes equation combined with an implicit time step technique. The new
scheme is positivity preserving, conditionally stable, consistent, and the order of the scheme
with respect to the space variable is two. Numerical investigations were conducted to validate
these results. Furthermore, the obtained results are more accurate than other existing results
in the literature.