Computational approach based on wavelets for financial mathematical model governed by distributed order fractional differential equation

Abstract

In this study, for the first time, the approximate solution of Black–Scholes option pricing distributed order time-fractional partial differential equation by means of Legendre and Chebyshev wavelets is considered. The operational matrices of Legendre and Chebyshev wavelets for integer order derivative and distributed order fractional derivative are derived. Furthermore, the combination of Gauss–Legendre quadrature formula and standard Tau method along with the obtained operational matrices reduces the distributed order time-fractional Black–Scholes model (DOTFBSM) into the system of linear algebraic equations. Convergence analysis, error bounds and numerical stability of the proposed approach are discussed in detail. The presented scheme is applied on three test examples and numerical experiments confirm the theoretical results and illustrate robustness of the presented method. The results produced by current approach are found to be more accurate than some available results. © 2021 International Association for Mathematics and Computers in Simulation (IMACS)