Multigrid Method for a Two Dimensional Fully Nonlinear Black-Scholes Equation with a Nonlinear Volatility Function (Journal of Mathematical Study, 2020)
This paper deals with the task of pricing European basket options in the presence of transaction costs. We develop a model that incorporates the illiquidity ofthe market into the classical two-assets Black-Scholes framework. We perform a numerical simulation using finite difference method. We consider a nonlinear multigridmethod in order to reduce computational costs. The objective of this paper is to investigate a deterministic extension for the Barles' and Soner's model and to demonstratethe effectiveness of multigrid approach to solving a fully nonlinear two dimensionalBlack-Scholes problem.