An Unconditionally Stable, Positivity-Preserving Splitting Scheme for Nonlinear Black-Scholes Equation with Transaction Costs. (7th May 2014)

• Record Type: Journal Article
• Authors: Guo, Jianqiang; Wang, Wansheng
• Other Names: Cheng Yumin Academic Editor.
• Is Part Of: TheScientificWorldjournal. Volume 2014(2014)
• Publication Date: 2014-05-07
• Subjects: Science -- Periodicals; Technology -- Periodicals; Medicine -- Periodicals; 505
• DOI: 10.1155/2014/525207
• Languages: English
• ISSNs: 2356-6140

Abstract

Abstract : This paper deals with the numerical analysis of nonlinear Black-Scholes equation with transaction costs. An unconditionally stable and monotone splitting method, ensuring positive numerical solution and avoiding unstable oscillations, is proposed. This numerical method is based on the LOD-Backward Euler method which allows us to solve the discrete equation explicitly. The numerical results for vanilla call option and for European butterfly spread are provided. It turns out that the proposed scheme is efficient and reliable.