Accuracy, Robustness, and Efficiency of the Linear Boundary Condition for the Black-Scholes Equations
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...
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| Main Authors: | , , , , , |
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
2015-01-01
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| Series: | Discrete Dynamics in Nature and Society |
| Online Access: | http://dx.doi.org/10.1155/2015/359028 |
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| _version_ | 1832558121205104640 |
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| author | Darae Jeong Seungsuk Seo Hyeongseok Hwang Dongsun Lee Yongho Choi Junseok Kim |
| author_facet | Darae Jeong Seungsuk Seo Hyeongseok Hwang Dongsun Lee Yongho Choi Junseok Kim |
| author_sort | Darae Jeong |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-a52f289c1db449da9122db449c2dcdab |
| institution | Kabale University |
| issn | 1026-0226 1607-887X |
| language | English |
| publishDate | 2015-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Discrete Dynamics in Nature and Society |
| spelling | doaj-art-a52f289c1db449da9122db449c2dcdab2025-02-03T01:33:18ZengWileyDiscrete Dynamics in Nature and Society1026-02261607-887X2015-01-01201510.1155/2015/359028359028Accuracy, Robustness, and Efficiency of the Linear Boundary Condition for the Black-Scholes EquationsDarae Jeong0Seungsuk Seo1Hyeongseok Hwang2Dongsun Lee3Yongho Choi4Junseok Kim5Department of Mathematics, Korea University, Seoul 136-713, Republic of KoreaGaram Analytics, Seodaemun, Seoul 120-749, Republic of KoreaDepartment of Financial Engineering, Korea University, Seoul 136-701, Republic of KoreaDepartment of Mathematics, Korea University, Seoul 136-713, Republic of KoreaDepartment of Mathematics, Korea University, Seoul 136-713, Republic of KoreaDepartment of Mathematics, Korea University, Seoul 136-713, Republic of KoreaWe 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.http://dx.doi.org/10.1155/2015/359028 |
| spellingShingle | Darae Jeong Seungsuk Seo Hyeongseok Hwang Dongsun Lee Yongho Choi Junseok Kim Accuracy, Robustness, and Efficiency of the Linear Boundary Condition for the Black-Scholes Equations Discrete Dynamics in Nature and Society |
| title | Accuracy, Robustness, and Efficiency of the Linear Boundary Condition for the Black-Scholes Equations |
| title_full | Accuracy, Robustness, and Efficiency of the Linear Boundary Condition for the Black-Scholes Equations |
| title_fullStr | Accuracy, Robustness, and Efficiency of the Linear Boundary Condition for the Black-Scholes Equations |
| title_full_unstemmed | Accuracy, Robustness, and Efficiency of the Linear Boundary Condition for the Black-Scholes Equations |
| title_short | Accuracy, Robustness, and Efficiency of the Linear Boundary Condition for the Black-Scholes Equations |
| title_sort | accuracy robustness and efficiency of the linear boundary condition for the black scholes equations |
| url | http://dx.doi.org/10.1155/2015/359028 |
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