NUMERICAL SOLUTION FOR FRACTIONAL BLACK-SCHOLES MODEL OF AMERICAN PUT OPTION PRICING

In this paper, we introduce a mathematical modeling of American put option pricing under the Fractional Black-Scholes model, which leads to a fractional partial differential equation with free boundary condition (the American option is an option that could be exercised at any time during the life of option). Then the free boundary (optimal exercise boundary) that is unknown, is found by using the quasi-stationary method that cause the Amer- ican put option pricing problem to be a solvable boundary value problem. In continuation we use a finite difference method for the derivatives with respect to stock price, Grounwal Letnikov approx- imation for derivatives with respect to time variable and reach a fractional finite difference problem. We show that the set up fractional finite difference problem is stable and convergent. We also show that the numerical result satisfy the physical conditions of American put option pricing under the Fractional Black-Scholes (FBS) model.