An Unconditionally Stable, Positivity-Preserving Splitting Scheme for Nonlinear Black-Scholes Equation with Transaction Costs

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 E...

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Bibliographic Details
Main Authors: Jianqiang Guo, Wansheng Wang
Format: Article
Language:English
Published: Wiley 2014-01-01
Series:The Scientific World Journal
Online Access:http://dx.doi.org/10.1155/2014/525207
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Summary: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.
ISSN:2356-6140
1537-744X