Nonlinear Black-Scholes equations arise from considering parameters such as feedback
and illiquid markets eects or large investor preferences, volatile portfolio and nontrivial
transaction costs into option pricing models to have more accurate option price. Here
some nite dierence schemes have been investigated to solve numerically such nonlinear
equations.
However the analytical solution of the linear Black-Scholes equation is known, dierent
numerical methods have been considered for solving the equation to make a general numerical
scheme for solving other more complicated models with no analytical solutions
such as nonlinear Black-Scholes models. Therefore at rst some investigations for the
standard linear Black-Scholes equation have been considered for instance choosing a suitable
right boundary condition and applying some remedies for dealing with nonsmooth
conditions of the equation. After that a number of nonlinear Black-Scholes models are
reviewed and dierent numerical methods have been investigated for solving some of
those models. At the end the numerical schemes have been compared with respect to
order of convergence.