Skip Navigation



IMA Journal of Numerical Analysis Advance Access published online on July 1, 2009
IMA Journal of Numerical Analysis, doi:10.1093/imanum/drp016
This Article
Right arrow Full Text (PDF)
Right arrow Alert me when this article is cited
Right arrow Alert me if a correction is posted
Services
Right arrow Email this article to a friend
Right arrow Similar articles in this journal
Right arrow Alert me to new issues of the journal
Right arrow Add to My Personal Archive
Right arrow Download to citation manager
Right arrowRequest Permissions
Google Scholar
Right arrow Articles by Huang, C.-S.
Right arrow Articles by Wang, S.
Social Bookmarking
Add to CiteULike   Add to Connotea   Add to Del.icio.us  
What's this?

© The author 2009. Published by Oxford University Press on behalf of the Institute of Mathematics and its Applications. All rights reserved.

On convergence of a fitted finite-volume method for the valuation of options on assets with stochastic volatilities

C.-S. Huang and C.-H. Hung{dagger}

Department of Applied Mathematics, National Sun Yat-sen University, No. 70, Lianhai Road, Gushan District, Kaohsiung City 804, Taiwan

Song Wang

Department of Mathematics and Statistics, The University of Western Australia, 35 Stirling Highway, Crawley WA6009, Australia

{dagger} Email: hungch{at}math.nsysu.edu.tw

Received on 3 July 2008. Revised on 23 March 2009.


  Abstract

In this paper we present a convergence analysis for a fitted finite-volume discretization method for the two-dimensional Black–Scholes equation arising in the Hull–White model for pricing European options with stochastic volatility. We first formulate the finite-volume method as a nonconforming Petrov–Galerkin finite–element method with each basis function of the trial space being determined by a set of two-point boundary-value problems defined on element edges. We then show that the bilinear form of the finite-element method is coercive and continuous. Finally we establish an upper bound of order Formula (h) on the discretization error of method, where h denotes the mesh parameter of the discretization.

Key Words: stochastic volatility; European option pricing; finite-volume method; stability and convergence


Add to CiteULike CiteULike   Add to Connotea Connotea   Add to Del.icio.us Del.icio.us    What's this?




Disclaimer: Please note that abstracts for content published before 1996 were created through digital scanning and may therefore not exactly replicate the text of the original print issues. All efforts have been made to ensure accuracy, but the Publisher will not be held responsible for any remaining inaccuracies. If you require any further clarification, please contact our Customer Services Department.