A Robust Numerical Scheme for Pricing American Options Under Regime Switching Based on Penalty Method
This paper is devoted to develop a robust numerical method to solve a system of complementarity problems (CPs) arising from pricing American options under regime switching. Based on a penalty method, the system of complementarity problems are approximated by a set of coupled nonlinear partial differ...
| Main Authors: | , , |
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| Format: | Journal Article |
| Published: |
Springer US
2013
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| Online Access: | http://hdl.handle.net/20.500.11937/42188 |
| _version_ | 1848756351187025920 |
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| author | Zhang, Kai Teo, Kok Lay Swartz, Mick |
| author_facet | Zhang, Kai Teo, Kok Lay Swartz, Mick |
| author_sort | Zhang, Kai |
| building | Curtin Institutional Repository |
| collection | Online Access |
| description | This paper is devoted to develop a robust numerical method to solve a system of complementarity problems (CPs) arising from pricing American options under regime switching. Based on a penalty method, the system of complementarity problems are approximated by a set of coupled nonlinear partial differential equations (PDEs). We then introduce a fitted finite volume (FFVM) method for the spatial discretization along with a fully implicit time stepping scheme for the PDEs, which results in a system of nonlinear algebraic equations. We show that this scheme is consistent, stable and monotone, hence convergent. To solve the system of nonlinear equations effectively, an iterative solution method is established. The convergence of the solution method is shown. Numerical tests are performed to examine the convergence rate and verify the effectiveness and robustness of the new numerical scheme. |
| first_indexed | 2025-11-14T09:10:49Z |
| format | Journal Article |
| id | curtin-20.500.11937-42188 |
| institution | Curtin University Malaysia |
| institution_category | Local University |
| last_indexed | 2025-11-14T09:10:49Z |
| publishDate | 2013 |
| publisher | Springer US |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | curtin-20.500.11937-421882017-09-13T14:19:39Z A Robust Numerical Scheme for Pricing American Options Under Regime Switching Based on Penalty Method Zhang, Kai Teo, Kok Lay Swartz, Mick Finite Volume Method American Option Pricing Regime Switching Penalty Method This paper is devoted to develop a robust numerical method to solve a system of complementarity problems (CPs) arising from pricing American options under regime switching. Based on a penalty method, the system of complementarity problems are approximated by a set of coupled nonlinear partial differential equations (PDEs). We then introduce a fitted finite volume (FFVM) method for the spatial discretization along with a fully implicit time stepping scheme for the PDEs, which results in a system of nonlinear algebraic equations. We show that this scheme is consistent, stable and monotone, hence convergent. To solve the system of nonlinear equations effectively, an iterative solution method is established. The convergence of the solution method is shown. Numerical tests are performed to examine the convergence rate and verify the effectiveness and robustness of the new numerical scheme. 2013 Journal Article http://hdl.handle.net/20.500.11937/42188 10.1007/s10614-013-9361-3 Springer US restricted |
| spellingShingle | Finite Volume Method American Option Pricing Regime Switching Penalty Method Zhang, Kai Teo, Kok Lay Swartz, Mick A Robust Numerical Scheme for Pricing American Options Under Regime Switching Based on Penalty Method |
| title | A Robust Numerical Scheme for Pricing American Options Under Regime Switching Based on Penalty Method |
| title_full | A Robust Numerical Scheme for Pricing American Options Under Regime Switching Based on Penalty Method |
| title_fullStr | A Robust Numerical Scheme for Pricing American Options Under Regime Switching Based on Penalty Method |
| title_full_unstemmed | A Robust Numerical Scheme for Pricing American Options Under Regime Switching Based on Penalty Method |
| title_short | A Robust Numerical Scheme for Pricing American Options Under Regime Switching Based on Penalty Method |
| title_sort | robust numerical scheme for pricing american options under regime switching based on penalty method |
| topic | Finite Volume Method American Option Pricing Regime Switching Penalty Method |
| url | http://hdl.handle.net/20.500.11937/42188 |