positive method for discrete double barrier options

The solution of the black-scholes partial differential equation determinesthe option price, respectively according to the used initial conditions. in the computation of the fair price of an option, it is a natural demand that the resulting numericalapproximations, should be non-negative. numerical methods based on standard finitedifference approach such as fully implicit, crank-nicolson, and semi-implicit schemesare powerful tools for pricing. they are usually consistent with the original differentialequation and guarantee convergency of the discrete solution to the exact one, but inthe presence of discontinuous payoff and low volatility, essential qualitative propertiesof the solution are not transferred to the numerical solution. spurious oscillations andnegative values might occur in the solution the application of a nonstandard finite difference method and investigation of its positivity preserving and smoothing properties forpricing european call options with a discrete double barrier is the subject of this paper.the new scheme is positivity preserving, conditionally stable, consistent, and convergent.some numerical experiments have been performed to illustrate the efficiency of the newscheme.