A robust numerical solution to a time-fractional Black–Scholes equation

Abstract Dividend paying European stock options are modeled using a time-fractional Black–Scholes (tfBS) partial differential equation (PDE). The underlying fractional stochastic dynamics explored in this work appropriate for capturing market fluctuations which random white noise has the potential to accurately estimate put option premiums while providing good numerical convergence. aim of paper is two fold: firstly, construct PDE pricing on continuous dividend stocks, and, secondly, propose an implicit finite difference method solving constructed tfBS PDE. Through rigorous mathematical analysis it established that scheme unconditionally stable. To support these theoretical observations, examples presented under proposed framework. Results indicate and its very effective tools options.