Multigrid Method for a Two Dimensional Fully Nonlinear Black-Scholes Equation with a Nonlinear Volatility Function
Year: 2020
Author: Aicha Driouch, Hassan Al Moatassime
Journal of Mathematical Study, Vol. 53 (2020), Iss. 3 : pp. 247–264
Abstract
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' and Soner's model and to demonstrate the effectiveness of multigrid approach to solving a fully nonlinear two dimensional Black-Scholes problem.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/jms.v53n3.20.02
Journal of Mathematical Study, Vol. 53 (2020), Iss. 3 : pp. 247–264
Published online: 2020-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 18
Keywords: Fully nonlinear equation multigrid method black-scholes equation finite difference method FAS algorithm.