The Artificial Boundary Problem Of Fractional American Option Black-Scholes Equation

In the classical approach the price of an asset is described by the celebrated Black-Scholes models.In this paper we consider a generalization of this model,which captures the subdiffusive characteristics of financial markets.We introduces a fast numerical method for computing American option pricing problems governed by this generalized Black-Scholes equation.The treatment of the free boundary is based on some properties of the solutions of the fractional Black-Scholes equation.An artificial boundary condition,which involves the time-fractional derivatives,is also used at the other end of the domain.An efficient finite difference approximation for the reduced initial-boundary problem on the space bounded domain is constructed.The stability and convergence of the finite difference approximation has been analysed.