A Review of Multilevel Monte Carlo Methods
| dc.contributor.advisor | McWalter, Thomas | |
| dc.contributor.author | Jain, Rohin | |
| dc.date.accessioned | 2021-02-02T19:48:25Z | |
| dc.date.available | 2021-02-02T19:48:25Z | |
| dc.date.issued | 2020 | |
| dc.date.updated | 2021-01-29T08:20:08Z | |
| dc.description.abstract | 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. | |
| dc.identifier.apacitation | Jain, R. (2020). <i>A Review of Multilevel Monte Carlo Methods</i>. (). ,Faculty of Commerce ,African Institute of Financial Markets and Risk Management. Retrieved from http://hdl.handle.net/11427/32754 | en_ZA |
| dc.identifier.chicagocitation | Jain, Rohin. <i>"A Review of Multilevel Monte Carlo Methods."</i> ., ,Faculty of Commerce ,African Institute of Financial Markets and Risk Management, 2020. http://hdl.handle.net/11427/32754 | en_ZA |
| dc.identifier.citation | Jain, R. 2020. A Review of Multilevel Monte Carlo Methods. . ,Faculty of Commerce ,African Institute of Financial Markets and Risk Management. http://hdl.handle.net/11427/32754 | en_ZA |
| dc.identifier.ris | TY - Master Thesis AU - Jain, Rohin AB - 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. DA - 2020_ DB - OpenUCT DP - University of Cape Town KW - Mathematical Finance LK - https://open.uct.ac.za PY - 2020 T1 - A Review of Multilevel Monte Carlo Methods TI - A Review of Multilevel Monte Carlo Methods UR - http://hdl.handle.net/11427/32754 ER - | en_ZA |
| dc.identifier.uri | http://hdl.handle.net/11427/32754 | |
| dc.identifier.vancouvercitation | Jain R. A Review of Multilevel Monte Carlo Methods. []. ,Faculty of Commerce ,African Institute of Financial Markets and Risk Management, 2020 [cited yyyy month dd]. Available from: http://hdl.handle.net/11427/32754 | en_ZA |
| dc.language.rfc3066 | eng | |
| dc.publisher.department | African Institute of Financial Markets and Risk Management | |
| dc.publisher.faculty | Faculty of Commerce | |
| dc.subject | Mathematical Finance | |
| dc.title | A Review of Multilevel Monte Carlo Methods | |
| dc.type | Master Thesis | |
| dc.type.qualificationlevel | Masters | |
| dc.type.qualificationlevel | MPhil |