sinc functions with application to finance

In this paper, we consider Black-Scholes equation, that arises in the American option model when thestock price follows a diffusionprocess with jump components. We use the sinc method to solve thisequation with its boundary conditions andfind thenumerical solution of the generalized Black–Scholespartial differential equation.The advantage of our method is that the sinc functions satisfies theboundary conditions and vanishes in infinity. This method has simple programing and gives thegoodResult compared to the previous methods. The quadrature, based on sinc functions, is veryaccurate and can be used to approximate the neededintegrals.

Keywords:

American option , Jump diffusion process , sinc function , sinc method