Penalty approach to a nonlinear obstacle problem governing American put option valuation under transaction costs
We propose a penalty method for a finite-dimensional nonlinear complementarity problem (NCP) arising from the discretization of the infinite-dimensional free boundary/obstacle problem governing the valuation of American options under transaction costs. In this method, the NCP is approximated by a sy...
| Main Authors: | , |
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| Format: | Journal Article |
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Elsevier
2015
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| Online Access: | http://hdl.handle.net/20.500.11937/46891 |
| _version_ | 1848757685826093056 |
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| author | Lesmana, D. Wang, Song |
| author_facet | Lesmana, D. Wang, Song |
| author_sort | Lesmana, D. |
| building | Curtin Institutional Repository |
| collection | Online Access |
| description | We propose a penalty method for a finite-dimensional nonlinear complementarity problem (NCP) arising from the discretization of the infinite-dimensional free boundary/obstacle problem governing the valuation of American options under transaction costs. In this method, the NCP is approximated by a system of nonlinear equations containing a power penalty term. We show that the mapping involved in the system is continuous and strongly monotone. Thus, the unique solvability of both the NCP and the penalty equation and the exponential convergence of the solution to the penalty equation to that of the NCP are guaranteed by an existing theory. Numerical results will be presented to demonstrate the convergence rates and usefulness of this penalty method. |
| first_indexed | 2025-11-14T09:32:02Z |
| format | Journal Article |
| id | curtin-20.500.11937-46891 |
| institution | Curtin University Malaysia |
| institution_category | Local University |
| last_indexed | 2025-11-14T09:32:02Z |
| publishDate | 2015 |
| publisher | Elsevier |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | curtin-20.500.11937-468912017-09-13T14:03:56Z Penalty approach to a nonlinear obstacle problem governing American put option valuation under transaction costs Lesmana, D. Wang, Song American option pricing Convergence Nonlinear Black–Scholes operator Nonlinear complementarity problem Penalty method Obstacle problem We propose a penalty method for a finite-dimensional nonlinear complementarity problem (NCP) arising from the discretization of the infinite-dimensional free boundary/obstacle problem governing the valuation of American options under transaction costs. In this method, the NCP is approximated by a system of nonlinear equations containing a power penalty term. We show that the mapping involved in the system is continuous and strongly monotone. Thus, the unique solvability of both the NCP and the penalty equation and the exponential convergence of the solution to the penalty equation to that of the NCP are guaranteed by an existing theory. Numerical results will be presented to demonstrate the convergence rates and usefulness of this penalty method. 2015 Journal Article http://hdl.handle.net/20.500.11937/46891 10.1016/j.amc.2014.11.060 Elsevier restricted |
| spellingShingle | American option pricing Convergence Nonlinear Black–Scholes operator Nonlinear complementarity problem Penalty method Obstacle problem Lesmana, D. Wang, Song Penalty approach to a nonlinear obstacle problem governing American put option valuation under transaction costs |
| title | Penalty approach to a nonlinear obstacle problem governing American put option valuation under transaction costs |
| title_full | Penalty approach to a nonlinear obstacle problem governing American put option valuation under transaction costs |
| title_fullStr | Penalty approach to a nonlinear obstacle problem governing American put option valuation under transaction costs |
| title_full_unstemmed | Penalty approach to a nonlinear obstacle problem governing American put option valuation under transaction costs |
| title_short | Penalty approach to a nonlinear obstacle problem governing American put option valuation under transaction costs |
| title_sort | penalty approach to a nonlinear obstacle problem governing american put option valuation under transaction costs |
| topic | American option pricing Convergence Nonlinear Black–Scholes operator Nonlinear complementarity problem Penalty method Obstacle problem |
| url | http://hdl.handle.net/20.500.11937/46891 |