Accuracy, robustness, and efficiency of the linear boundary condition for the black-scholes equations

Darae Jeong; Seungsuk Seo; Hyeongseok Hwang; Dongsun Lee; Yongho Choi; Junseok Kim

doi:10.1155/2015/359028

Accuracy, robustness, and efficiency of the linear boundary condition for the black-scholes equations

Darae Jeong, Seungsuk Seo, Hyeongseok Hwang, Dongsun Lee, Yongho Choi, Junseok Kim

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

7 Citations (Scopus)

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.

Original language	English
Article number	359028
Journal	Discrete Dynamics in Nature and Society
Volume	2015
DOIs	https://doi.org/10.1155/2015/359028
Publication status	Published - 2015

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Publisher Copyright:
© 2015 Darae Jeong et al.

ASJC Scopus subject areas

Modelling and Simulation

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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.",

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AU - Seo, Seungsuk

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AU - Lee, Dongsun

AU - Choi, Yongho

AU - Kim, Junseok

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AB - 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.

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Accuracy, robustness, and efficiency of the linear boundary condition for the black-scholes equations

Abstract

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