Rough Paths based Numerical Algorithms in Computational Finance.
The paper connects asymptotic estimations of [3] and [7] with the Rough Paths perspective ([13], [14]) to present a general framework for deriving high order, stable and tractable path-wise approximations of stochastic differential equations. The approach, which can be traced back to [17] and probab...
| Main Authors: | , |
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| Formato: | Working paper |
| Idioma: | English |
| Publicado em: |
Oxford-Man Institute of Quantitative Finance
2008
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| _version_ | 1826294052146905088 |
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| author | Gyurkó, L Lyons, T |
| author_facet | Gyurkó, L Lyons, T |
| author_sort | Gyurkó, L |
| collection | OXFORD |
| description | The paper connects asymptotic estimations of [3] and [7] with the Rough Paths perspective ([13], [14]) to present a general framework for deriving high order, stable and tractable path-wise approximations of stochastic differential equations. The approach, which can be traced back to [17] and probably earlier, is based on locally deriving and solving random ordinary differential equations. A sufficient condition on the accuracy of the numerical ODE solver is given to ensure the global order is g1/2 if the local order is g. We also point out some practical solutions which make the high order schemes tractable. |
| first_indexed | 2024-03-07T03:39:41Z |
| format | Working paper |
| id | oxford-uuid:bd73ea11-c1a6-4e42-a64c-df265358d4a7 |
| institution | University of Oxford |
| language | English |
| last_indexed | 2024-03-07T03:39:41Z |
| publishDate | 2008 |
| publisher | Oxford-Man Institute of Quantitative Finance |
| record_format | dspace |
| spelling | oxford-uuid:bd73ea11-c1a6-4e42-a64c-df265358d4a72022-03-27T05:31:57ZRough Paths based Numerical Algorithms in Computational Finance.Working paperhttp://purl.org/coar/resource_type/c_8042uuid:bd73ea11-c1a6-4e42-a64c-df265358d4a7EnglishDepartment of Economics - ePrintsOxford-Man Institute of Quantitative Finance2008Gyurkó, LLyons, TThe paper connects asymptotic estimations of [3] and [7] with the Rough Paths perspective ([13], [14]) to present a general framework for deriving high order, stable and tractable path-wise approximations of stochastic differential equations. The approach, which can be traced back to [17] and probably earlier, is based on locally deriving and solving random ordinary differential equations. A sufficient condition on the accuracy of the numerical ODE solver is given to ensure the global order is g1/2 if the local order is g. We also point out some practical solutions which make the high order schemes tractable. |
| spellingShingle | Gyurkó, L Lyons, T Rough Paths based Numerical Algorithms in Computational Finance. |
| title | Rough Paths based Numerical Algorithms in Computational Finance. |
| title_full | Rough Paths based Numerical Algorithms in Computational Finance. |
| title_fullStr | Rough Paths based Numerical Algorithms in Computational Finance. |
| title_full_unstemmed | Rough Paths based Numerical Algorithms in Computational Finance. |
| title_short | Rough Paths based Numerical Algorithms in Computational Finance. |
| title_sort | rough paths based numerical algorithms in computational finance |
| work_keys_str_mv | AT gyurkol roughpathsbasednumericalalgorithmsincomputationalfinance AT lyonst roughpathsbasednumericalalgorithmsincomputationalfinance |