Pricing European options with proportional transaction costs and stochastic volatility using a penalty approach and a finite volume scheme
© 2017 Elsevier Ltd In this paper we propose a combination of a penalty method and a finite volume scheme for a four-dimensional time-dependent Hamilton–Jacobi–Bellman (HJB) equation arising from pricing European options with proportional transaction costs and stochastic volatility. The HJB equation...
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| Format: | Journal Article |
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Pergamon Press
2017
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| Online Access: | http://hdl.handle.net/20.500.11937/56074 |
| _version_ | 1848759780384964608 |
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| author | Li, W. Wang, Song |
| author_facet | Li, W. Wang, Song |
| author_sort | Li, W. |
| building | Curtin Institutional Repository |
| collection | Online Access |
| description | © 2017 Elsevier Ltd In this paper we propose a combination of a penalty method and a finite volume scheme for a four-dimensional time-dependent Hamilton–Jacobi–Bellman (HJB) equation arising from pricing European options with proportional transaction costs and stochastic volatility. The HJB equation is first approximated by a nonlinear partial differential equation containing penalty terms. A finite volume method along with an upwind technique is then developed for the spatial discretization of the nonlinear penalty equation. We show that the coefficient matrix of the discretized system is an M-matrix. An iterative method is proposed for solving the nonlinear algebraic system and a convergence theory is established for the iterative method. Numerical experiments are performed using a non-trivial model pricing problem and the numerical results demonstrate the usefulness of the proposed method. |
| first_indexed | 2025-11-14T10:05:19Z |
| format | Journal Article |
| id | curtin-20.500.11937-56074 |
| institution | Curtin University Malaysia |
| institution_category | Local University |
| last_indexed | 2025-11-14T10:05:19Z |
| publishDate | 2017 |
| publisher | Pergamon Press |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | curtin-20.500.11937-560742017-09-13T16:09:54Z Pricing European options with proportional transaction costs and stochastic volatility using a penalty approach and a finite volume scheme Li, W. Wang, Song © 2017 Elsevier Ltd In this paper we propose a combination of a penalty method and a finite volume scheme for a four-dimensional time-dependent Hamilton–Jacobi–Bellman (HJB) equation arising from pricing European options with proportional transaction costs and stochastic volatility. The HJB equation is first approximated by a nonlinear partial differential equation containing penalty terms. A finite volume method along with an upwind technique is then developed for the spatial discretization of the nonlinear penalty equation. We show that the coefficient matrix of the discretized system is an M-matrix. An iterative method is proposed for solving the nonlinear algebraic system and a convergence theory is established for the iterative method. Numerical experiments are performed using a non-trivial model pricing problem and the numerical results demonstrate the usefulness of the proposed method. 2017 Journal Article http://hdl.handle.net/20.500.11937/56074 10.1016/j.camwa.2017.03.024 Pergamon Press restricted |
| spellingShingle | Li, W. Wang, Song Pricing European options with proportional transaction costs and stochastic volatility using a penalty approach and a finite volume scheme |
| title | Pricing European options with proportional transaction costs and stochastic volatility using a penalty approach and a finite volume scheme |
| title_full | Pricing European options with proportional transaction costs and stochastic volatility using a penalty approach and a finite volume scheme |
| title_fullStr | Pricing European options with proportional transaction costs and stochastic volatility using a penalty approach and a finite volume scheme |
| title_full_unstemmed | Pricing European options with proportional transaction costs and stochastic volatility using a penalty approach and a finite volume scheme |
| title_short | Pricing European options with proportional transaction costs and stochastic volatility using a penalty approach and a finite volume scheme |
| title_sort | pricing european options with proportional transaction costs and stochastic volatility using a penalty approach and a finite volume scheme |
| url | http://hdl.handle.net/20.500.11937/56074 |