Convergence of the Saul’yev scheme for European option pricing with transaction costs nonlinear equation

The nonlinear Black-Scholes equation has been increasingly attracting interest over the last two decades , because it provides more accurate values by considering transaction costs as a viable assumptions . In this paper the Saul’yev finite difference scheme for fully nonlinear Black- Scholes equation is analyzed . It is shown that the Saul’yev finite difference scheme converges to the unique viscosity solution of the continuous equation . The result is based on a study of the stability , monotonicity and consistency of the scheme .