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A Review of Multilevel Monte Carlo Methods
The Monte Carlo method (MC) is a common numerical technique used to approximate an expectation that does not have an analytical solution. For certain problems, MC can be inefficient. Many techniques exist to improve the efficiency of MC methods. The Multilevel Monte Carlo (ML) technique developed Gi...
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| Format: | Thesis |
| Language: | English |
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African Institute of Financial Markets and Risk Management
2021
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| _version_ | 1867613203578486784 |
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| access_status_str | Open Access |
| author | Jain, Rohin |
| author2 | McWalter, Thomas |
| author_browse | Jain, Rohin McWalter, Thomas |
| author_facet | McWalter, Thomas Jain, Rohin |
| author_sort | Jain, Rohin |
| collection | Thesis |
| description | The Monte Carlo method (MC) is a common numerical technique used to approximate an expectation that does not have an analytical solution. For certain problems, MC can be inefficient. Many techniques exist to improve the efficiency of MC methods. The Multilevel Monte Carlo (ML) technique developed Giles (2008) is one such method. It relies on approximating the payoff at different levels of accuracy and using a telescoping sum of these approximations to compute the ML estimator. This dissertation summarises the ML technique and its implementation. To start with, the framework is applied to a European call option. Results show that the efficiency of the method is up to 13 times faster than crude MC. Then an American put option is priced within the ML framework using two pricing methods. The Least Squares Monte Carlo method (LSM) estimates an optimal exercise strategy at finitely many instances, and consequently a lower bound price for the option. The dual method finds an optimal martingale, and consequently an upper bound for the price. Although the pricing results are quite close to the corresponding crude MC method, the efficiency produces mixed results. The LSM method performs poorly within an ML framework, while the dual approach is enhanced. |
| format | Thesis |
| id | oai:open.uct.ac.za:11427/32754 |
| institution | University of Cape Town (South Africa) |
| language | eng |
| last_indexed | 2026-06-10T12:32:24.523Z |
| license_str | Not specified — see source repository |
| provenance_str_mv | Harvested via OAI-PMH from UCTD — University of Cape Town Open Access Repository |
| publishDate | 2021 |
| publishDateRange | 2021 |
| publishDateSort | 2021 |
| publisher | African Institute of Financial Markets and Risk Management |
| publisherStr | African Institute of Financial Markets and Risk Management |
| record_format | dspace |
| source_str | UCTD — University of Cape Town Open Access Repository |
| spelling | oai:open.uct.ac.za:11427/32754 A Review of Multilevel Monte Carlo Methods Jain, Rohin McWalter, Thomas Mathematical Finance The Monte Carlo method (MC) is a common numerical technique used to approximate an expectation that does not have an analytical solution. For certain problems, MC can be inefficient. Many techniques exist to improve the efficiency of MC methods. The Multilevel Monte Carlo (ML) technique developed Giles (2008) is one such method. It relies on approximating the payoff at different levels of accuracy and using a telescoping sum of these approximations to compute the ML estimator. This dissertation summarises the ML technique and its implementation. To start with, the framework is applied to a European call option. Results show that the efficiency of the method is up to 13 times faster than crude MC. Then an American put option is priced within the ML framework using two pricing methods. The Least Squares Monte Carlo method (LSM) estimates an optimal exercise strategy at finitely many instances, and consequently a lower bound price for the option. The dual method finds an optimal martingale, and consequently an upper bound for the price. Although the pricing results are quite close to the corresponding crude MC method, the efficiency produces mixed results. The LSM method performs poorly within an ML framework, while the dual approach is enhanced. 2021-02-02T19:48:25Z 2021-02-02T19:48:25Z 2020 2021-01-29T08:20:08Z Master Thesis Masters MPhil http://hdl.handle.net/11427/32754 eng application/pdf African Institute of Financial Markets and Risk Management Faculty of Commerce |
| spellingShingle | Mathematical Finance Jain, Rohin A Review of Multilevel Monte Carlo Methods |
| thesis_degree_str | Master's |
| title | A Review of Multilevel Monte Carlo Methods |
| title_full | A Review of Multilevel Monte Carlo Methods |
| title_fullStr | A Review of Multilevel Monte Carlo Methods |
| title_full_unstemmed | A Review of Multilevel Monte Carlo Methods |
| title_short | A Review of Multilevel Monte Carlo Methods |
| title_sort | review of multilevel monte carlo methods |
| topic | Mathematical Finance |
| url | http://hdl.handle.net/11427/32754 |
| work_keys_str_mv | AT jainrohin areviewofmultilevelmontecarlomethods AT jainrohin reviewofmultilevelmontecarlomethods |