Accuracy, Robustness, and Efficiency of the Linear Boundary Condition for the Black-Scholes Equations. (2nd March 2015)

• Record Type: Journal Article
• Authors: Jeong, Darae; Seo, Seungsuk; Hwang, Hyeongseok; Lee, Dongsun; Choi, Yongho; Kim, Junseok
• Other Names: He Xiao-Qiao Academic Editor.
• Is Part Of: Discrete dynamics in nature and society. Volume 2015(2015)
• Publication Date: 2015-03-02
• Subjects: System analysis -- Periodicals; Dynamics -- Periodicals; Chaotic behavior in systems -- Periodicals; Differentiable dynamical systems -- Periodicals; 003.05
• DOI: 10.1155/2015/359028
• Languages: English
• ISSNs: 1026-0226

Abstract

Abstract : We briefly review and investigate the performance of various boundary conditions such as Dirichlet, Neumann, linear, and partial differential equation boundary conditions for the numerical solutions of the Black-Scholes partial differential equation. We use a finite difference method to numerically solve the equation. To show the efficiency of the given boundary condition, several numerical examples are presented. In numerical test, we investigate the effect of the domain sizes and compare the effect of various boundary conditions with pointwise error and root mean square error. Numerical results show that linear boundary condition is accurate and efficient among the other boundary conditions.