A finite difference method for pricing European and American options under a geometric Lévy process
In this paper we develop a numerical approach to a fractional-order differential Linear Complementarity Problem (LCP) arising in pricing European and American options under a geometric Lévy process. The LCP is first approximated by a nonlinear penalty fractional Black-Scholes (fBS) equation. We then...
| Main Authors: | , |
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| Format: | Journal Article |
| Published: |
2015
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| Online Access: | http://hdl.handle.net/20.500.11937/40837 |
| _version_ | 1848755978329128960 |
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| author | Chen, W. Wang, Song |
| author_facet | Chen, W. Wang, Song |
| author_sort | Chen, W. |
| building | Curtin Institutional Repository |
| collection | Online Access |
| description | In this paper we develop a numerical approach to a fractional-order differential Linear Complementarity Problem (LCP) arising in pricing European and American options under a geometric Lévy process. The LCP is first approximated by a nonlinear penalty fractional Black-Scholes (fBS) equation. We then propose a finite difference scheme for the penalty fBS equation. We show that both the continuous and the discretized fBS equations are uniquely solvable and establish the convergence of the numerical solution to the viscosity solution of the penalty fBS equation by proving the consistency, stability and monotonicity of the numerical scheme. We also show that the discretization has the 2nd-order truncation error in both the spatial and time mesh sizes. Numerical results are presented to demonstrate the accuracy and usefulness of the numerical method for pricing both European and American options under the geometric Lévy process. |
| first_indexed | 2025-11-14T09:04:53Z |
| format | Journal Article |
| id | curtin-20.500.11937-40837 |
| institution | Curtin University Malaysia |
| institution_category | Local University |
| last_indexed | 2025-11-14T09:04:53Z |
| publishDate | 2015 |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | curtin-20.500.11937-408372019-02-19T05:35:07Z A finite difference method for pricing European and American options under a geometric Lévy process Chen, W. Wang, Song In this paper we develop a numerical approach to a fractional-order differential Linear Complementarity Problem (LCP) arising in pricing European and American options under a geometric Lévy process. The LCP is first approximated by a nonlinear penalty fractional Black-Scholes (fBS) equation. We then propose a finite difference scheme for the penalty fBS equation. We show that both the continuous and the discretized fBS equations are uniquely solvable and establish the convergence of the numerical solution to the viscosity solution of the penalty fBS equation by proving the consistency, stability and monotonicity of the numerical scheme. We also show that the discretization has the 2nd-order truncation error in both the spatial and time mesh sizes. Numerical results are presented to demonstrate the accuracy and usefulness of the numerical method for pricing both European and American options under the geometric Lévy process. 2015 Journal Article http://hdl.handle.net/20.500.11937/40837 10.3934/jimo.2015.11.241 fulltext |
| spellingShingle | Chen, W. Wang, Song A finite difference method for pricing European and American options under a geometric Lévy process |
| title | A finite difference method for pricing European and American options under a geometric Lévy process |
| title_full | A finite difference method for pricing European and American options under a geometric Lévy process |
| title_fullStr | A finite difference method for pricing European and American options under a geometric Lévy process |
| title_full_unstemmed | A finite difference method for pricing European and American options under a geometric Lévy process |
| title_short | A finite difference method for pricing European and American options under a geometric Lévy process |
| title_sort | finite difference method for pricing european and american options under a geometric lévy process |
| url | http://hdl.handle.net/20.500.11937/40837 |