A class of fourth-order Padé schemes for fractional exotic options pricing model

In order to reduce the oscillations of the numerical solution of fractional exotic options pricing model, a class of numerical schemes are developed and well studied in this paper which are based on the 4th-order Padé approximation and 2nd-order weighted and shifted Grünwald difference scheme. Since the spatial discretization matrix is positive definite and has lower Hessenberg Toeplitz structure, we prove the convergence of the proposed scheme. Numerical experiments on fractional digital option and fractional barrier options show that the (0, 4)-Padé scheme is fast, and significantly reduces the oscillations of the solution and smooths the Delta value.