Analysing multi-level Monte Carlo for options with non-globally Lipschitz payoff
Giles (Oper. Res. 56:607-617, 2008) introduced a multi-level Monte Carlo method for approximating the expected value of a function of a stochastic differential equation solution. A key application is to compute the expected payoff of a financial option. This new method improves on the computational...
| Main Authors: | , , |
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| Formato: | Journal article |
| Idioma: | English |
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2009
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| _version_ | 1826290522215415808 |
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| author | Giles, M Higham, D Mao, X |
| author_facet | Giles, M Higham, D Mao, X |
| author_sort | Giles, M |
| collection | OXFORD |
| description | Giles (Oper. Res. 56:607-617, 2008) introduced a multi-level Monte Carlo method for approximating the expected value of a function of a stochastic differential equation solution. A key application is to compute the expected payoff of a financial option. This new method improves on the computational complexity of standard Monte Carlo. Giles analysed globally Lipschitz payoffs, but also found good performance in practice for non-globally Lipschitz cases. In this work, we show that the multi-level Monte Carlo method can be rigorously justified for non-globally Lipschitz payoffs. In particular, we consider digital, lookback and barrier options. This requires non-standard strong convergence analysis of the Euler-Maruyama method. © Springer-Verlag 2009. |
| first_indexed | 2024-03-07T02:45:28Z |
| format | Journal article |
| id | oxford-uuid:abe8ac05-4687-4a02-9845-703e3b51eebe |
| institution | University of Oxford |
| language | English |
| last_indexed | 2024-03-07T02:45:28Z |
| publishDate | 2009 |
| record_format | dspace |
| spelling | oxford-uuid:abe8ac05-4687-4a02-9845-703e3b51eebe2022-03-27T03:25:07ZAnalysing multi-level Monte Carlo for options with non-globally Lipschitz payoffJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:abe8ac05-4687-4a02-9845-703e3b51eebeEnglishSymplectic Elements at Oxford2009Giles, MHigham, DMao, XGiles (Oper. Res. 56:607-617, 2008) introduced a multi-level Monte Carlo method for approximating the expected value of a function of a stochastic differential equation solution. A key application is to compute the expected payoff of a financial option. This new method improves on the computational complexity of standard Monte Carlo. Giles analysed globally Lipschitz payoffs, but also found good performance in practice for non-globally Lipschitz cases. In this work, we show that the multi-level Monte Carlo method can be rigorously justified for non-globally Lipschitz payoffs. In particular, we consider digital, lookback and barrier options. This requires non-standard strong convergence analysis of the Euler-Maruyama method. © Springer-Verlag 2009. |
| spellingShingle | Giles, M Higham, D Mao, X Analysing multi-level Monte Carlo for options with non-globally Lipschitz payoff |
| title | Analysing multi-level Monte Carlo for options with non-globally Lipschitz payoff |
| title_full | Analysing multi-level Monte Carlo for options with non-globally Lipschitz payoff |
| title_fullStr | Analysing multi-level Monte Carlo for options with non-globally Lipschitz payoff |
| title_full_unstemmed | Analysing multi-level Monte Carlo for options with non-globally Lipschitz payoff |
| title_short | Analysing multi-level Monte Carlo for options with non-globally Lipschitz payoff |
| title_sort | analysing multi level monte carlo for options with non globally lipschitz payoff |
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