Multi-level 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 an Euler discretisation, the computational cost to achiev...
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| Médium: | Report |
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Unspecified
2006
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| _version_ | 1826272748881575936 |
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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 an Euler discretisation, the computational cost to achieve an accuracy of $O(\epsilon)$ is reduced from $O(\epsilon^{-3})$ to $O(\epsilon^{-2} (\log \epsilon)^2)$. The analysis is supported by numerical results showing significant computational savings. |
| first_indexed | 2024-03-06T22:17:30Z |
| format | Report |
| id | oxford-uuid:53e4f4f5-bf70-4c2f-aa8c-09b607e6c7f2 |
| institution | University of Oxford |
| last_indexed | 2024-03-06T22:17:30Z |
| publishDate | 2006 |
| publisher | Unspecified |
| record_format | dspace |
| spelling | oxford-uuid:53e4f4f5-bf70-4c2f-aa8c-09b607e6c7f22022-03-26T16:34:29ZMulti-level Monte Carlo path simulationReporthttp://purl.org/coar/resource_type/c_93fcuuid:53e4f4f5-bf70-4c2f-aa8c-09b607e6c7f2Mathematical Institute - ePrintsUnspecified2006Giles, 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 an Euler discretisation, the computational cost to achieve an accuracy of $O(\epsilon)$ is reduced from $O(\epsilon^{-3})$ to $O(\epsilon^{-2} (\log \epsilon)^2)$. The analysis is supported by numerical results showing significant computational savings. |
| spellingShingle | Giles, M Multi-level Monte Carlo path simulation |
| title | Multi-level Monte Carlo path simulation |
| title_full | Multi-level Monte Carlo path simulation |
| title_fullStr | Multi-level Monte Carlo path simulation |
| title_full_unstemmed | Multi-level Monte Carlo path simulation |
| title_short | Multi-level Monte Carlo path simulation |
| title_sort | multi level monte carlo path simulation |
| work_keys_str_mv | AT gilesm multilevelmontecarlopathsimulation |