The Convergence Rate of Option Prices in Trinomial Trees
We study the convergence of the binomial, trinomial, and more generally m-nomial tree schemes when evaluating certain European path-independent options in the Black–Scholes setting. To our knowledge, the results here are the first for trinomial trees. Our main result provides formulae for the coeffi...
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2023
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| Online Access: | https://hdl.handle.net/11073/33267 |
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| _version_ | 1864513431755816960 |
|---|---|
| author | Leduc, Guillaume |
| author2 | Palmer, Kenneth |
| author2_role | author |
| author_facet | Leduc, Guillaume Palmer, Kenneth |
| author_role | author |
| dc.creator.none.fl_str_mv | Leduc, Guillaume Palmer, Kenneth |
| dc.date.none.fl_str_mv | 2023-03-26 2026-03-25T10:31:59Z 2026-03-25T10:31:59Z |
| dc.format.none.fl_str_mv | application/pdf |
| dc.identifier.none.fl_str_mv | 2227-9091 https://hdl.handle.net/11073/33267 10.3390/risks11030052 |
| dc.language.none.fl_str_mv | en |
| dc.publisher.none.fl_str_mv | MDPI |
| dc.relation.none.fl_str_mv | Leduc, G., & Palmer, K. (2023). The Convergence Rate of Option Prices in Trinomial Trees. Risks, 11(3), 52. https://doi.org/10.3390/risks11030052 |
| dc.rights.none.fl_str_mv | Attribution 4.0 International http://creativecommons.org/licenses/by/4.0/ |
| dc.subject.none.fl_str_mv | Option Pricing Trinomial Tree Asymptotic Expansion Edgeworth Series |
| dc.title.none.fl_str_mv | The Convergence Rate of Option Prices in Trinomial Trees |
| dc.type.none.fl_str_mv | Peer-Reviewed Published version info:eu-repo/semantics/publishedVersion info:eu-repo/semantics/article |
| description | We study the convergence of the binomial, trinomial, and more generally m-nomial tree schemes when evaluating certain European path-independent options in the Black–Scholes setting. To our knowledge, the results here are the first for trinomial trees. Our main result provides formulae for the coefficients of 1/−−√ and 1/ in the expansion of the error for digital and standard put and call options. This result is obtained from an Edgeworth series in the form of Kolassa–McCullagh, which we derive from a recently established Edgeworth series in the form of Esseen/Bhattacharya and Rao for triangular arrays of random variables. We apply our result to the most popular trinomial trees and provide numerical illustrations. |
| format | article |
| id | aus_4c9aacd3961b872013ab0db9d0cc68a3 |
| identifier_str_mv | 2227-9091 10.3390/risks11030052 |
| language_invalid_str_mv | en |
| network_acronym_str | aus |
| network_name_str | aus |
| oai_identifier_str | oai:repository.aus.edu:11073/33267 |
| publishDate | 2023 |
| 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 | The Convergence Rate of Option Prices in Trinomial TreesLeduc, GuillaumePalmer, KennethOption PricingTrinomial TreeAsymptotic ExpansionEdgeworth SeriesWe study the convergence of the binomial, trinomial, and more generally m-nomial tree schemes when evaluating certain European path-independent options in the Black–Scholes setting. To our knowledge, the results here are the first for trinomial trees. Our main result provides formulae for the coefficients of 1/−−√ and 1/ in the expansion of the error for digital and standard put and call options. This result is obtained from an Edgeworth series in the form of Kolassa–McCullagh, which we derive from a recently established Edgeworth series in the form of Esseen/Bhattacharya and Rao for triangular arrays of random variables. We apply our result to the most popular trinomial trees and provide numerical illustrations.MDPI2026-03-25T10:31:59Z2026-03-25T10:31:59Z2023-03-26Peer-ReviewedPublished versioninfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articleapplication/pdf2227-9091https://hdl.handle.net/11073/3326710.3390/risks11030052enLeduc, G., & Palmer, K. (2023). The Convergence Rate of Option Prices in Trinomial Trees. Risks, 11(3), 52. https://doi.org/10.3390/risks11030052Attribution 4.0 Internationalhttp://creativecommons.org/licenses/by/4.0/oai:repository.aus.edu:11073/332672026-03-26T05:13:27Z |
| spellingShingle | The Convergence Rate of Option Prices in Trinomial Trees Leduc, Guillaume Option Pricing Trinomial Tree Asymptotic Expansion Edgeworth Series |
| status_str | publishedVersion |
| title | The Convergence Rate of Option Prices in Trinomial Trees |
| title_full | The Convergence Rate of Option Prices in Trinomial Trees |
| title_fullStr | The Convergence Rate of Option Prices in Trinomial Trees |
| title_full_unstemmed | The Convergence Rate of Option Prices in Trinomial Trees |
| title_short | The Convergence Rate of Option Prices in Trinomial Trees |
| title_sort | The Convergence Rate of Option Prices in Trinomial Trees |
| topic | Option Pricing Trinomial Tree Asymptotic Expansion Edgeworth Series |
| url | https://hdl.handle.net/11073/33267 |