TY - JOUR
T1 - Multigrid Method for a Two Dimensional Fully Nonlinear Black-Scholes Equation with a Nonlinear Volatility Function
AU - Driouch , Aicha
AU - Moatassime , Hassan Al
JO - Journal of Mathematical Study
VL - 3
SP - 247
EP - 264
PY - 2020
DA - 2020/05
SN - 53
DO - http://doi.org/10.4208/jms.v53n3.20.02
UR - https://global-sci.org/intro/article_detail/jms/16919.html
KW - Fully nonlinear equation, multigrid method, black-scholes equation, finite difference method, FAS algorithm.
AB - <p style="text-align: justify;">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 of
the market into the classical two-assets Black-Scholes framework. We perform a numerical simulation using finite difference method. We consider a nonlinear multigrid
method in order to reduce computational costs. The objective of this paper is to investigate a deterministic extension for the Barles&#39; and Soner&#39;s model and to demonstrate
the effectiveness of multigrid approach to solving a fully nonlinear two dimensional
Black-Scholes problem.</p>