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Volume 53, Issue 3
Multigrid Method for a Two Dimensional Fully Nonlinear Black-Scholes Equation with a Nonlinear Volatility Function

Aicha Driouch & Hassan Al Moatassime

DOI: 10.4208/jms.v53n3.20.02

J. Math. Study, 53 (2020), pp. 247-264.

Published online: 2020-05

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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.

  • Keywords

Fully nonlinear equation, multigrid method, black-scholes equation, finite difference method, FAS algorithm.

  • AMS Subject Headings

65N55, 65N06, 35K55, 65BXX

  • Copyright

COPYRIGHT: © Global Science Press

  • Email address

driouch.aicha@gmail.com (Aicha Driouch)

hassan.al.moatassime@gmail.com (Hassan Al Moatassime)

  • BibTex
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@Article{JMS-53-247, author = {Driouch , Aicha and Moatassime , Hassan Al}, title = {Multigrid Method for a Two Dimensional Fully Nonlinear Black-Scholes Equation with a Nonlinear Volatility Function}, journal = {Journal of Mathematical Study}, year = {2020}, volume = {53}, number = {3}, pages = {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.

}, issn = {2617-8702}, doi = {https://doi.org/10.4208/jms.v53n3.20.02}, url = {http://global-sci.org/intro/article_detail/jms/16919.html} }
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 -

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.

Driouch , Aicha and Moatassime , Hassan Al. (2020). Multigrid Method for a Two Dimensional Fully Nonlinear Black-Scholes Equation with a Nonlinear Volatility Function. Journal of Mathematical Study. 53 (3). 247-264. doi:10.4208/jms.v53n3.20.02
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