A Closed Form Series Solution for Nonlinear Black–Scholes Equation

In this paper, we consider the illiquid European call option which is arisen in nonlinear Black–Scholes equation. In this respect, we apply the Newton’s method to linearize it. Based on the obtained linear problem, we implement the Fourier transform and by attention to the hedging parameters of the Black–Scholes equation, we get analytical solution recursively in two steps. Finally, we investigate the convergence condition of the desired solution based on the Kantorovich theorem. The numerical results show that our algorithm is best performed and concordance with similar papers