Multigrid Method for a Two Dimensional Fully Nonlinear Black-Scholes Equation with a Nonlinear Volatility Function |
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| Authors: | Aicha Driouch & Hassan Al Moatassime |
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| 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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| Keywords: | Fully nonlinear equation multigrid method black-scholes equation finite difference method FAS algorithm |
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