A new operator splitting method for American options under fractional Black–Scholes models

Abstract

A new operator splitting method is proposed for American options under time-fractional Black–Scholes models. The fractional linear complementarity problem is split into two easy sub-problems, with the leading coefficients separated from the convolution sum and matched through a general correction step. The method is implementation friendly in the sense that one can easily modify a fractional European solver to obtain the proposed method, since the correction step is decoupled and is trivial to solve. The method is validated through numerical experiments and demonstrated to be superior to the traditional approach. The paper also provides numerical studies including the effect of fractional orders and the comparison of fractional models.