Robust numerical algorithm to the European option with illiquid markets

Abstract

In this paper, we consider 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 equation, we obtain the approximate solutions recursively in two steps. Finally, based on the conditions of Kantorovich theorem, we investigate the convergence analysis of the Newton’s method on the proposed problem. Finally the positivity of the solution is discussed.