A 2nd-order FDM for a 2D fractional black-scholes equation

Abstract

© Springer International Publishing AG 2017. We develop a finite difference method (FDM) for a 2D fractional Black-Scholes equation arising in the optimal control problem of pricing European options on two assets under two independent geometric Lévy processes. We establish the convergence of the method by showing that the FDM is consistent, stable and monotone. We also show that the truncation error of the FDM is of 2nd order. Numerical experiments demonstrate that the method produces financially meaningful results when used for solving practical problems.