Convergence Speed of Bermudan, Randomized Bermudan, and Canadian Options
American options have long received considerable attention in the literature, with numerous publications dedicated to their pricing. Bermudan and randomized Bermudan options are broadly used to estimate their prices efficiently. Notably, the penalty method yields option prices that coincide with tho...
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| المؤلف الرئيسي: | |
|---|---|
| التنسيق: | article |
| منشور في: |
2025
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| الموضوعات: | |
| الوصول للمادة أونلاين: | https://hdl.handle.net/11073/25772 |
| الوسوم: |
إضافة وسم
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| _version_ | 1864513434032275456 |
|---|---|
| author | Leduc, Guillaume |
| author_facet | Leduc, Guillaume |
| author_role | author |
| dc.creator.none.fl_str_mv | Leduc, Guillaume |
| dc.date.none.fl_str_mv | 2025-01-20T07:40:04Z 2025-01-20T07:40:04Z 2025-01-10 |
| dc.format.none.fl_str_mv | application/pdf |
| dc.identifier.none.fl_str_mv | Leduc, G. (2025). Convergence Speed of Bermudan, Randomized Bermudan, and Canadian Options. Mathematics, 13(2), 213. https://doi.org/10.3390/math13020213 2227-7390 https://hdl.handle.net/11073/25772 10.3390/math13020213 |
| dc.language.none.fl_str_mv | en |
| dc.publisher.none.fl_str_mv | MDPI |
| dc.relation.none.fl_str_mv | https://doi.org/10.3390/math13020213 |
| dc.rights.none.fl_str_mv | Attribution 4.0 International http://creativecommons.org/licenses/by/4.0/ |
| dc.subject.none.fl_str_mv | Bermudan option American option Randomization Convergence speed |
| dc.title.none.fl_str_mv | Convergence Speed of Bermudan, Randomized Bermudan, and Canadian Options |
| dc.type.none.fl_str_mv | Peer-Reviewed Published version info:eu-repo/semantics/publishedVersion info:eu-repo/semantics/article |
| description | American options have long received considerable attention in the literature, with numerous publications dedicated to their pricing. Bermudan and randomized Bermudan options are broadly used to estimate their prices efficiently. Notably, the penalty method yields option prices that coincide with those of randomized Bermudan options. However, theoretical results regarding the speed of convergence of these approximations to the American option price remain scarce. In this paper, we address this gap by establishing a general result on the convergence speed of Bermudan and randomized Bermudan option prices to their American limits. We prove that for convex payoff functions, the convergence speed is linear; that is, of order 1/n, where n denotes the number of exercisable opportunities in the Bermudan case and serves as the intensity parameter of the underlying Poisson process in the randomized Bermudan case. Our framework is quite general, encompassing Lévy models, stochastic volatility models, and nearly any risk-neutral model that can be incorporated within a strong Markov framework. We extend our analysis to Canadian options, showing under mild conditions a convergence rate of 1/√n to their American limits. To our knowledge, this is the first study addressing the speed of convergence in Canadian option pricing. |
| format | article |
| id | aus_3335ea2fa1f4075fd6a342ee72cb51ad |
| identifier_str_mv | Leduc, G. (2025). Convergence Speed of Bermudan, Randomized Bermudan, and Canadian Options. Mathematics, 13(2), 213. https://doi.org/10.3390/math13020213 2227-7390 10.3390/math13020213 |
| language_invalid_str_mv | en |
| network_acronym_str | aus |
| network_name_str | aus |
| oai_identifier_str | oai:repository.aus.edu:11073/25772 |
| publishDate | 2025 |
| publisher.none.fl_str_mv | MDPI |
| repository.mail.fl_str_mv | |
| repository.name.fl_str_mv | |
| repository_id_str | |
| rights_invalid_str_mv | Attribution 4.0 International http://creativecommons.org/licenses/by/4.0/ |
| spelling | Convergence Speed of Bermudan, Randomized Bermudan, and Canadian OptionsLeduc, GuillaumeBermudan optionAmerican optionRandomizationConvergence speedAmerican options have long received considerable attention in the literature, with numerous publications dedicated to their pricing. Bermudan and randomized Bermudan options are broadly used to estimate their prices efficiently. Notably, the penalty method yields option prices that coincide with those of randomized Bermudan options. However, theoretical results regarding the speed of convergence of these approximations to the American option price remain scarce. In this paper, we address this gap by establishing a general result on the convergence speed of Bermudan and randomized Bermudan option prices to their American limits. We prove that for convex payoff functions, the convergence speed is linear; that is, of order 1/n, where n denotes the number of exercisable opportunities in the Bermudan case and serves as the intensity parameter of the underlying Poisson process in the randomized Bermudan case. Our framework is quite general, encompassing Lévy models, stochastic volatility models, and nearly any risk-neutral model that can be incorporated within a strong Markov framework. We extend our analysis to Canadian options, showing under mild conditions a convergence rate of 1/√n to their American limits. To our knowledge, this is the first study addressing the speed of convergence in Canadian option pricing.MDPI2025-01-20T07:40:04Z2025-01-20T07:40:04Z2025-01-10Peer-ReviewedPublished versioninfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articleapplication/pdfLeduc, G. (2025). Convergence Speed of Bermudan, Randomized Bermudan, and Canadian Options. Mathematics, 13(2), 213. https://doi.org/10.3390/math130202132227-7390https://hdl.handle.net/11073/2577210.3390/math13020213enhttps://doi.org/10.3390/math13020213Attribution 4.0 Internationalhttp://creativecommons.org/licenses/by/4.0/oai:repository.aus.edu:11073/257722025-01-21T15:04:50Z |
| spellingShingle | Convergence Speed of Bermudan, Randomized Bermudan, and Canadian Options Leduc, Guillaume Bermudan option American option Randomization Convergence speed |
| status_str | publishedVersion |
| title | Convergence Speed of Bermudan, Randomized Bermudan, and Canadian Options |
| title_full | Convergence Speed of Bermudan, Randomized Bermudan, and Canadian Options |
| title_fullStr | Convergence Speed of Bermudan, Randomized Bermudan, and Canadian Options |
| title_full_unstemmed | Convergence Speed of Bermudan, Randomized Bermudan, and Canadian Options |
| title_short | Convergence Speed of Bermudan, Randomized Bermudan, and Canadian Options |
| title_sort | Convergence Speed of Bermudan, Randomized Bermudan, and Canadian Options |
| topic | Bermudan option American option Randomization Convergence speed |
| url | https://hdl.handle.net/11073/25772 |