Analysis of multilevel Monte Carlo path simulation using the Milstein discretisation
The multilevel Monte Carlo path simulation method introduced by Giles (Operations Research, 56(3):607-617, 2008) exploits strong convergence properties to improve the computational complexity by combining simulations with different levels of resolution. In this paper we analyse its efficiency when u...
| Auteurs principaux: | , , |
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| Format: | Journal article |
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American Institute of Mathematical Sciences
2019
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| _version_ | 1826278876530081792 |
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| author | Giles, M Debrabant, K Roessler, A |
| author_facet | Giles, M Debrabant, K Roessler, A |
| author_sort | Giles, M |
| collection | OXFORD |
| description | The multilevel Monte Carlo path simulation method introduced by Giles (Operations Research, 56(3):607-617, 2008) exploits strong convergence properties to improve the computational complexity by combining simulations with different levels of resolution. In this paper we analyse its efficiency when using the Milstein discretisation; this has an improved order of strong convergence compared to the standard Euler-Maruyama method, and it is proved that this leads to an improved order of convergence of the variance of the multilevel estimator. Numerical results are also given for basket options to illustrate the relevance of the analysis. |
| first_indexed | 2024-03-06T23:50:30Z |
| format | Journal article |
| id | oxford-uuid:726fab5a-8c92-4b9e-9eeb-3ba7010607c7 |
| institution | University of Oxford |
| last_indexed | 2024-03-06T23:50:30Z |
| publishDate | 2019 |
| publisher | American Institute of Mathematical Sciences |
| record_format | dspace |
| spelling | oxford-uuid:726fab5a-8c92-4b9e-9eeb-3ba7010607c72022-03-26T19:50:03ZAnalysis of multilevel Monte Carlo path simulation using the Milstein discretisationJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:726fab5a-8c92-4b9e-9eeb-3ba7010607c7Symplectic Elements at OxfordAmerican Institute of Mathematical Sciences2019Giles, MDebrabant, KRoessler, AThe multilevel Monte Carlo path simulation method introduced by Giles (Operations Research, 56(3):607-617, 2008) exploits strong convergence properties to improve the computational complexity by combining simulations with different levels of resolution. In this paper we analyse its efficiency when using the Milstein discretisation; this has an improved order of strong convergence compared to the standard Euler-Maruyama method, and it is proved that this leads to an improved order of convergence of the variance of the multilevel estimator. Numerical results are also given for basket options to illustrate the relevance of the analysis. |
| spellingShingle | Giles, M Debrabant, K Roessler, A Analysis of multilevel Monte Carlo path simulation using the Milstein discretisation |
| title | Analysis of multilevel Monte Carlo path simulation using the Milstein discretisation |
| title_full | Analysis of multilevel Monte Carlo path simulation using the Milstein discretisation |
| title_fullStr | Analysis of multilevel Monte Carlo path simulation using the Milstein discretisation |
| title_full_unstemmed | Analysis of multilevel Monte Carlo path simulation using the Milstein discretisation |
| title_short | Analysis of multilevel Monte Carlo path simulation using the Milstein discretisation |
| title_sort | analysis of multilevel monte carlo path simulation using the milstein discretisation |
| work_keys_str_mv | AT gilesm analysisofmultilevelmontecarlopathsimulationusingthemilsteindiscretisation AT debrabantk analysisofmultilevelmontecarlopathsimulationusingthemilsteindiscretisation AT roesslera analysisofmultilevelmontecarlopathsimulationusingthemilsteindiscretisation |