A High‐Order Operator‐Splitting Method for Solving Time‐Fractional American Option Pricing

ABSTRACT

In this paper, we develop a computational technique for a Caputo time‐fractional Black–Scholes (TFBS) equation governing the American options. The nonuniform technique is employed in the temporal direction, while a fourth‐order compact difference scheme is used in the spatial direction. Moreover, an operator‐splitting method is used to deal with the free boundary arising in the American options model. A rigorous stability analysis of the proposed scheme is performed. The convergence analysis of the proposed scheme is presented, establishing a temporal convergence rate of and a fourth‐order convergence rate in the spatial direction. The practical applicability of the scheme is demonstrated by solving a financial test problem involving the pricing of American put options. A comparative analysis is conducted with existing methods in the literature to show the advantage of the proposed method. More specifically, we compare the computed results with those obtained by the methods based on LU decomposition and operator‐splitting techniques given in the literature.