Measure order of convergence without an exact solution, Euler vs Milstein scheme
The purpose of this paper is to measure the strong and weak order of convergence of both the Euler and Milstein schemes using a stochastic volatility model and an N−dimensional Exponential Brownian Motion Process (EBM). An exact solution is normally required to calculate the order of convergence, ho...
| Main Authors: | , |
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| פורמט: | Journal article |
| יצא לאור: |
2005
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| _version_ | 1826274139281817600 |
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| author | Schmitz Abe, K Shaw, W |
| author_facet | Schmitz Abe, K Shaw, W |
| author_sort | Schmitz Abe, K |
| collection | OXFORD |
| description | The purpose of this paper is to measure the strong and weak order of convergence of both the Euler and Milstein schemes using a stochastic volatility model and an N−dimensional Exponential Brownian Motion Process (EBM). An exact solution is normally required to calculate the order of convergence, however there are none available for this volatility process. We propose a method to solve this problem. We also show numerically that when we apply the Milstein scheme to an N−dimensional stochastic process, there is a need to take into account the correlation between the systems. |
| first_indexed | 2024-03-06T22:38:54Z |
| format | Journal article |
| id | oxford-uuid:5adb9d0d-3bfa-4217-9e46-a2c77465074d |
| institution | University of Oxford |
| last_indexed | 2024-03-06T22:38:54Z |
| publishDate | 2005 |
| record_format | dspace |
| spelling | oxford-uuid:5adb9d0d-3bfa-4217-9e46-a2c77465074d2022-03-26T17:18:26ZMeasure order of convergence without an exact solution, Euler vs Milstein schemeJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:5adb9d0d-3bfa-4217-9e46-a2c77465074dMathematical Institute - ePrints2005Schmitz Abe, KShaw, WThe purpose of this paper is to measure the strong and weak order of convergence of both the Euler and Milstein schemes using a stochastic volatility model and an N−dimensional Exponential Brownian Motion Process (EBM). An exact solution is normally required to calculate the order of convergence, however there are none available for this volatility process. We propose a method to solve this problem. We also show numerically that when we apply the Milstein scheme to an N−dimensional stochastic process, there is a need to take into account the correlation between the systems. |
| spellingShingle | Schmitz Abe, K Shaw, W Measure order of convergence without an exact solution, Euler vs Milstein scheme |
| title | Measure order of convergence without an exact solution, Euler vs Milstein scheme |
| title_full | Measure order of convergence without an exact solution, Euler vs Milstein scheme |
| title_fullStr | Measure order of convergence without an exact solution, Euler vs Milstein scheme |
| title_full_unstemmed | Measure order of convergence without an exact solution, Euler vs Milstein scheme |
| title_short | Measure order of convergence without an exact solution, Euler vs Milstein scheme |
| title_sort | measure order of convergence without an exact solution euler vs milstein scheme |
| work_keys_str_mv | AT schmitzabek measureorderofconvergencewithoutanexactsolutioneulervsmilsteinscheme AT shaww measureorderofconvergencewithoutanexactsolutioneulervsmilsteinscheme |