On the numerical solution of nonlinear option pricing equation in illiquid markets

In this paper we focus on the numerical solution of nonlinear Black–Scholes equation modeling illiquid markets. Two monotone unconditionally stable splitting methods, ensuring positive numerical solution and avoiding unstable oscillations, are applied to solve nonlinear Black–Scholes equation modeling illiquid markets. These numerical methods are based on the LOD methods which allow us to solve the discrete equation explicitly. The properties of these methods are analyzed. The numerical results for vanilla call option are compared to the local Crank–Nicolson scheme. The numerical results for European butterfly spread are also provided.