Semismooth Newton methods with domain decomposition for American options
type: Item
instance of: scholarly article
title: Semismooth Newton methods with domain decomposition for American options
zbMATH Open document ID: 1461.91362
author: Hong-Jie Zhao
author: Haijian Yang
published in: Journal of Computational and Applied Mathematics
publication date: 2018-05-04T00:00:00Z
review text: The authors consider a class of parallel semismooth Newton algorithms for the numerical solution of the American option under the Black-Scholes-Merton pricing framework. A nonlinear function is used to transform the complementarity problem, which arises from the discretization of the pricing model, into a nonlinear system. More precisely, the authors consider a more general class of semismooth Newton methods and some highly parallel domain decomposition methods for the American option. In addition, an adaptive time stepping technique, which adjusts the time step size according to the initial residual of Newton iterations is applied to improve the performance of the proposed numerical method. The effectiveness and scalability of the proposed algorithm depend heavily on the design of the preconditioner. It is shown that the class of additive Schwarz method works well, and is more attractive than the traditional preconditioners. Numerical results for several test cases showed that the proposed algorithm is robust and superior to the classical methods.
reviewed by: Nikolay Kyurkchiev
Mathematics Subject Classification ID: 91G60
Mathematics Subject Classification ID: 65M55
Mathematics Subject Classification ID: 91G20
Mathematics Subject Classification ID: 60G40
zbMATH DE Number: 6866620
zbMATH Keywords: American put option
zbMATH Keywords: semismooth Newton method
zbMATH Keywords: domain decomposition
zbMATH Keywords: additive Schwarz preconditioner
zbMATH Keywords: parallel computing
describes a project that uses: PETSc
MaRDI profile type: Publication
full work available at URL: j.cam.2017.12.046
OpenAlex ID: W2793304423
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DOI: 10.1016/J.CAM.2017.12.046
description: scientific article; zbMATH DE number 6866620