title: An unconditionally stable, positivity-preserving splitting scheme for nonlinear Black-Scholes equation with transaction costs.
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.
authors.affiliation: Law School, Hunan University, Hunan 410082, China.
authors.forename: Jianqiang
authors.initials: J
authors.lastname: Guo
authors.affiliation: School of Mathematics and Computational Science, Changsha University of Science and Technology, Hunan 410114, China.
authors.forename: Wansheng
authors.initials: W
authors.lastname: Wang
mesh_terms: D000465:Algorithms; D003365:Costs and Cost Analysis; D008962:Models, Theoretical