Convergence analysis of Crank-Nicolson and Rannacher time-marching
This paper presents a convergence analysis of Crank-Nicolson and Rannacher time-marching methods which are often used in finite difference discretisations of the Black-Scholes equations. Particular attention is paid to the important role of Rannacher's startup procedure, in which one or more in...
| المؤلفون الرئيسيون: | , |
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| التنسيق: | Report |
| منشور في: |
Unspecified
2005
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| _version_ | 1826301201222729728 |
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| author | Giles, M Carter, R |
| author_facet | Giles, M Carter, R |
| author_sort | Giles, M |
| collection | OXFORD |
| description | This paper presents a convergence analysis of Crank-Nicolson and Rannacher time-marching methods which are often used in finite difference discretisations of the Black-Scholes equations. Particular attention is paid to the important role of Rannacher's startup procedure, in which one or more initial timesteps use Backward Euler timestepping, to achieve second order convergence for approximations of the first and second derivatives. Numerical results confirm the sharpness of the error analysis which is based on asymptotic analysis of the behaviour of the Fourier transform. The relevance to Black-Scholes applications is discussed in detail, with numerical results supporting recommendations on how to maximise the accuracy for a given computational cost. |
| first_indexed | 2024-03-07T05:28:48Z |
| format | Report |
| id | oxford-uuid:e17ca056-6f7b-4e71-b4cd-a784805f4cf9 |
| institution | University of Oxford |
| last_indexed | 2024-03-07T05:28:48Z |
| publishDate | 2005 |
| publisher | Unspecified |
| record_format | dspace |
| spelling | oxford-uuid:e17ca056-6f7b-4e71-b4cd-a784805f4cf92022-03-27T09:54:49ZConvergence analysis of Crank-Nicolson and Rannacher time-marchingReporthttp://purl.org/coar/resource_type/c_93fcuuid:e17ca056-6f7b-4e71-b4cd-a784805f4cf9Mathematical Institute - ePrintsUnspecified2005Giles, MCarter, RThis paper presents a convergence analysis of Crank-Nicolson and Rannacher time-marching methods which are often used in finite difference discretisations of the Black-Scholes equations. Particular attention is paid to the important role of Rannacher's startup procedure, in which one or more initial timesteps use Backward Euler timestepping, to achieve second order convergence for approximations of the first and second derivatives. Numerical results confirm the sharpness of the error analysis which is based on asymptotic analysis of the behaviour of the Fourier transform. The relevance to Black-Scholes applications is discussed in detail, with numerical results supporting recommendations on how to maximise the accuracy for a given computational cost. |
| spellingShingle | Giles, M Carter, R Convergence analysis of Crank-Nicolson and Rannacher time-marching |
| title | Convergence analysis of Crank-Nicolson and Rannacher time-marching |
| title_full | Convergence analysis of Crank-Nicolson and Rannacher time-marching |
| title_fullStr | Convergence analysis of Crank-Nicolson and Rannacher time-marching |
| title_full_unstemmed | Convergence analysis of Crank-Nicolson and Rannacher time-marching |
| title_short | Convergence analysis of Crank-Nicolson and Rannacher time-marching |
| title_sort | convergence analysis of crank nicolson and rannacher time marching |
| work_keys_str_mv | AT gilesm convergenceanalysisofcranknicolsonandrannachertimemarching AT carterr convergenceanalysisofcranknicolsonandrannachertimemarching |