Applying the barycentric Jacobi spectral method to price options with transaction costs in a fractional Black-Scholes framework

Abstract

The aim of this paper is to show how options with transaction costs under fractional, mixed Brownian-fractional, and subdiffusive fractional Black-Scholes models can be efficiently computed by using the barycentric Jacobi spectral method. The reliability of the barycentric Jacobi spectral method for space (asset) direction discretiza-tion is demonstrated by solving partial differential equations (PDEs) arising from pricing European options with transaction costs under these models. The discretization of these PDEs in time relies on the implicit Runge-Kutta Radau IIA method. We conducted various numerical experiments and compared our numerical results with ex-isting analytical solutions. It was found that the proposed method is efficient, highly accurate and reliable, and is an alternative to some existing numerical methods for pricing financial options.