Multilevel Monte Carlo path simulation
We show that multigrid ideas can be used to reduce the computational complexity of estimating an expected value arising from a stochastic differential equation using Monte Carlo path simulations. In the simplest case of a Lipschitz payoff and a Euler discretisation, the computational cost to achieve...
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| Format: | Journal article |
| Language: | English |
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2008
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| _version_ | 1826258447603073024 |
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| author | Giles, M |
| author_facet | Giles, M |
| author_sort | Giles, M |
| collection | OXFORD |
| description | We show that multigrid ideas can be used to reduce the computational complexity of estimating an expected value arising from a stochastic differential equation using Monte Carlo path simulations. In the simplest case of a Lipschitz payoff and a Euler discretisation, the computational cost to achieve an accuracy of O(ε) is reduced from O(ε-3) to O(ε-2(logε)2). The analysis is supported, by numerical results showing significant computational savings. © 2008 INFORMS. |
| first_indexed | 2024-03-06T18:34:09Z |
| format | Journal article |
| id | oxford-uuid:0aa80ab7-9406-4778-8f1a-cdafc9c1ed9b |
| institution | University of Oxford |
| language | English |
| last_indexed | 2024-03-06T18:34:09Z |
| publishDate | 2008 |
| record_format | dspace |
| spelling | oxford-uuid:0aa80ab7-9406-4778-8f1a-cdafc9c1ed9b2022-03-26T09:25:00ZMultilevel Monte Carlo path simulationJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:0aa80ab7-9406-4778-8f1a-cdafc9c1ed9bEnglishSymplectic Elements at Oxford2008Giles, MWe show that multigrid ideas can be used to reduce the computational complexity of estimating an expected value arising from a stochastic differential equation using Monte Carlo path simulations. In the simplest case of a Lipschitz payoff and a Euler discretisation, the computational cost to achieve an accuracy of O(ε) is reduced from O(ε-3) to O(ε-2(logε)2). The analysis is supported, by numerical results showing significant computational savings. © 2008 INFORMS. |
| spellingShingle | Giles, M Multilevel Monte Carlo path simulation |
| title | Multilevel Monte Carlo path simulation |
| title_full | Multilevel Monte Carlo path simulation |
| title_fullStr | Multilevel Monte Carlo path simulation |
| title_full_unstemmed | Multilevel Monte Carlo path simulation |
| title_short | Multilevel Monte Carlo path simulation |
| title_sort | multilevel monte carlo path simulation |
| work_keys_str_mv | AT gilesm multilevelmontecarlopathsimulation |