A penalty-based method from reconstructing smooth local volatility surface from American options
This paper is devoted to develop a robust penalty-based method of reconstructing smooth local volatility surface from the observed American option prices. This reconstruction problem is posed as an inverse problem: given a nite set of observed American option prices, nd a local volatility function...
| Main Authors: | , |
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| Format: | Journal Article |
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American Institute of Mathematical Sciences
2015
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| Online Access: | http://hdl.handle.net/20.500.11937/3463 |
| _version_ | 1848744239082504192 |
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| author | Zhang, K. Teo, Kok Lay |
| author_facet | Zhang, K. Teo, Kok Lay |
| author_sort | Zhang, K. |
| building | Curtin Institutional Repository |
| collection | Online Access |
| description | This paper is devoted to develop a robust penalty-based method of reconstructing smooth local volatility surface from the observed American option prices. This reconstruction problem is posed as an inverse problem: given a nite set of observed American option prices, nd a local volatility function such that the theoretical option prices matches the observed ones optimally with respect to a prescribed performance criterion. The theoretical American option prices are governed by a set of partial dierential complementarity problems (PDCP). We propose a penalty-based numerical method for the solution of the PDCP. Typically, the reconstruction problem is ill-posed and a bicubic spline regularization technique is thus proposed to overcome this diculty. We apply a gradient-based optimization algorithm to solve this nonlinear optimization problem, where the Jacobian of the cost function is computed via nite dierence approximation. Two numerical experiments: a synthetic American put option example and a real market American put option example, are performed to show the robustness and eectiveness of the proposed method to reconstructing the unknown volatility surface. |
| first_indexed | 2025-11-14T05:58:18Z |
| format | Journal Article |
| id | curtin-20.500.11937-3463 |
| institution | Curtin University Malaysia |
| institution_category | Local University |
| last_indexed | 2025-11-14T05:58:18Z |
| publishDate | 2015 |
| publisher | American Institute of Mathematical Sciences |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | curtin-20.500.11937-34632017-09-13T16:06:10Z A penalty-based method from reconstructing smooth local volatility surface from American options Zhang, K. Teo, Kok Lay This paper is devoted to develop a robust penalty-based method of reconstructing smooth local volatility surface from the observed American option prices. This reconstruction problem is posed as an inverse problem: given a nite set of observed American option prices, nd a local volatility function such that the theoretical option prices matches the observed ones optimally with respect to a prescribed performance criterion. The theoretical American option prices are governed by a set of partial dierential complementarity problems (PDCP). We propose a penalty-based numerical method for the solution of the PDCP. Typically, the reconstruction problem is ill-posed and a bicubic spline regularization technique is thus proposed to overcome this diculty. We apply a gradient-based optimization algorithm to solve this nonlinear optimization problem, where the Jacobian of the cost function is computed via nite dierence approximation. Two numerical experiments: a synthetic American put option example and a real market American put option example, are performed to show the robustness and eectiveness of the proposed method to reconstructing the unknown volatility surface. 2015 Journal Article http://hdl.handle.net/20.500.11937/3463 10.3934/jimo.2015.11.631 American Institute of Mathematical Sciences unknown |
| spellingShingle | Zhang, K. Teo, Kok Lay A penalty-based method from reconstructing smooth local volatility surface from American options |
| title | A penalty-based method from reconstructing smooth local volatility surface from American options |
| title_full | A penalty-based method from reconstructing smooth local volatility surface from American options |
| title_fullStr | A penalty-based method from reconstructing smooth local volatility surface from American options |
| title_full_unstemmed | A penalty-based method from reconstructing smooth local volatility surface from American options |
| title_short | A penalty-based method from reconstructing smooth local volatility surface from American options |
| title_sort | penalty-based method from reconstructing smooth local volatility surface from american options |
| url | http://hdl.handle.net/20.500.11937/3463 |