Efficient High-Order Numerical Methods for Pricing of Options

In this paper we present efficient high-order methods based on weighted essentially non-oscillatory (WENO) technique and backward differencing formula (BDF) to solve the European and American put options of the Black–Scholes equation. In order to achieve high-order convergent and prevent the appearance of spurious solutions close to non-smooth points, the WENO method is imposed for the spatial discretization. To achieve the high-order accuracy in non-smooth points as well as smooth points, a grid stretching transformation is employed. For the numerical solution of American put option, a predictor–corrector scheme based on WENO and BDF is constructed. The high efficiency of proposed methods for the solution of European and American put options is demonstrated numerically. Comparisons are made with the available methods in the literature.