A numerical scheme for pricing american options with transaction costs under a jump diffusion process
In this paper we develop a numerical method for a nonlinear partial integro-differential complementarity problem arising from pricing American options with transaction costs when the underlying assets follow a jump diffusion process. We first approximate the complementarity problem by a nonlinear pa...
| Main Authors: | , |
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| Format: | Journal Article |
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American Institute of Mathematical Sciences
2017
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| Online Access: | http://hdl.handle.net/20.500.11937/58032 |
| _version_ | 1848760159528026112 |
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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 | In this paper we develop a numerical method for a nonlinear partial integro-differential complementarity problem arising from pricing American options with transaction costs when the underlying assets follow a jump diffusion process. We first approximate the complementarity problem by a nonlinear partial integro-differential equation (PIDE) using a penalty approach. The PIDE is then discretized by a combination of a spatial upwind finite differencing and a fully implicit time stepping scheme. We prove that the coeficient matrix of the system from this scheme is an M-matrix and that the approximate solution converges to the viscosity solution to the PIDE by showing that the scheme is consistent, monotone, and unconditionally stable. We also propose a Newton's iterative method coupled with a Fast Fourier Transform for the computation of the discretized integral term for solving the fully discretized system. Numerical results will be presented to demonstrate the convergence rates and usefulness of this method. |
| first_indexed | 2025-11-14T10:11:21Z |
| format | Journal Article |
| id | curtin-20.500.11937-58032 |
| institution | Curtin University Malaysia |
| institution_category | Local University |
| last_indexed | 2025-11-14T10:11:21Z |
| publishDate | 2017 |
| publisher | American Institute of Mathematical Sciences |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | curtin-20.500.11937-580322017-11-20T08:58:16Z A numerical scheme for pricing american options with transaction costs under a jump diffusion process Lesmana, D. Wang, Song In this paper we develop a numerical method for a nonlinear partial integro-differential complementarity problem arising from pricing American options with transaction costs when the underlying assets follow a jump diffusion process. We first approximate the complementarity problem by a nonlinear partial integro-differential equation (PIDE) using a penalty approach. The PIDE is then discretized by a combination of a spatial upwind finite differencing and a fully implicit time stepping scheme. We prove that the coeficient matrix of the system from this scheme is an M-matrix and that the approximate solution converges to the viscosity solution to the PIDE by showing that the scheme is consistent, monotone, and unconditionally stable. We also propose a Newton's iterative method coupled with a Fast Fourier Transform for the computation of the discretized integral term for solving the fully discretized system. Numerical results will be presented to demonstrate the convergence rates and usefulness of this method. 2017 Journal Article http://hdl.handle.net/20.500.11937/58032 10.3934/jimo.2017019 American Institute of Mathematical Sciences restricted |
| spellingShingle | Lesmana, D. Wang, Song A numerical scheme for pricing american options with transaction costs under a jump diffusion process |
| title | A numerical scheme for pricing american options with transaction costs under a jump diffusion process |
| title_full | A numerical scheme for pricing american options with transaction costs under a jump diffusion process |
| title_fullStr | A numerical scheme for pricing american options with transaction costs under a jump diffusion process |
| title_full_unstemmed | A numerical scheme for pricing american options with transaction costs under a jump diffusion process |
| title_short | A numerical scheme for pricing american options with transaction costs under a jump diffusion process |
| title_sort | numerical scheme for pricing american options with transaction costs under a jump diffusion process |
| url | http://hdl.handle.net/20.500.11937/58032 |