Path Independence of Exotic Options and Convergence of Binomial Approximations
The analysis of the convergence of tree methods for pricing barrier and lookback options has been the subject of numerous publications aiming at describing, quantifying, and improving the slow and oscillatory convergence in such methods. For barrier and lookback options, we find path-independent opt...
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| المؤلف الرئيسي: | |
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| مؤلفون آخرون: | |
| التنسيق: | article |
| منشور في: |
2019
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| الموضوعات: | |
| الوصول للمادة أونلاين: | http://hdl.handle.net/11073/16662 |
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إضافة وسم
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| _version_ | 1864513432832704512 |
|---|---|
| author | Leduc, Guillaume |
| author2 | Palmer, Kenneth J. |
| author2_role | author |
| author_facet | Leduc, Guillaume Palmer, Kenneth J. |
| author_role | author |
| dc.creator.none.fl_str_mv | Leduc, Guillaume Palmer, Kenneth J. |
| dc.date.none.fl_str_mv | 2019 2020-06-02T07:35:03Z 2020-06-02T07:35:03Z |
| dc.format.none.fl_str_mv | application/pdf |
| dc.identifier.none.fl_str_mv | Leduc, Guillaume, and Palmer, Kenneth. "Path independence of exotic options and convergence of binomial approximations." Journal of Computational Finance 23, no (2), (2019): 73-102. doi: 10.21314/JCF.2019.372. 1755-2850 http://hdl.handle.net/11073/16662 10.21314/JCF.2019.372. |
| dc.language.none.fl_str_mv | en_US |
| dc.publisher.none.fl_str_mv | Infopro Digital Risk (IP) |
| dc.relation.none.fl_str_mv | https://doi.org/10.21314/JCF.2019.372 |
| dc.subject.none.fl_str_mv | Black-Scholes Exotic Barrier Lookback Binomial Path dependence Convergence |
| dc.title.none.fl_str_mv | Path Independence of Exotic Options and Convergence of Binomial Approximations |
| dc.type.none.fl_str_mv | Peer-Reviewed Published version info:eu-repo/semantics/publishedVersion info:eu-repo/semantics/article |
| description | The analysis of the convergence of tree methods for pricing barrier and lookback options has been the subject of numerous publications aiming at describing, quantifying, and improving the slow and oscillatory convergence in such methods. For barrier and lookback options, we find path-independent options whose price is exactly that of the original path-dependent option. The usual binomial models converge at a speed of order 1∕√ to the Black-Scholes price. Our new path-independent approach yields convergence of order 1∕. Furthermore, we derive a closed form formula for the coefficient of 1∕ in the expansion of the error of our path-independent pricing when the underlying is approximated by the Cox, Ross, and Rubinstein (CRR) model. Using this we obtain a corrected model with a convergence of order ⁻³/² to the price of barrier and lookback options in the Black-Scholes model. Our results are supported and illustrated by numerical examples. |
| format | article |
| id | aus_22692b2d6ec9eba17b9b013368f37173 |
| identifier_str_mv | Leduc, Guillaume, and Palmer, Kenneth. "Path independence of exotic options and convergence of binomial approximations." Journal of Computational Finance 23, no (2), (2019): 73-102. doi: 10.21314/JCF.2019.372. 1755-2850 10.21314/JCF.2019.372. |
| language_invalid_str_mv | en_US |
| network_acronym_str | aus |
| network_name_str | aus |
| oai_identifier_str | oai:repository.aus.edu:11073/16662 |
| publishDate | 2019 |
| publisher.none.fl_str_mv | Infopro Digital Risk (IP) |
| repository.mail.fl_str_mv | |
| repository.name.fl_str_mv | |
| repository_id_str | |
| spelling | Path Independence of Exotic Options and Convergence of Binomial ApproximationsLeduc, GuillaumePalmer, Kenneth J.Black-ScholesExoticBarrierLookbackBinomialPath dependenceConvergenceThe analysis of the convergence of tree methods for pricing barrier and lookback options has been the subject of numerous publications aiming at describing, quantifying, and improving the slow and oscillatory convergence in such methods. For barrier and lookback options, we find path-independent options whose price is exactly that of the original path-dependent option. The usual binomial models converge at a speed of order 1∕√ to the Black-Scholes price. Our new path-independent approach yields convergence of order 1∕. Furthermore, we derive a closed form formula for the coefficient of 1∕ in the expansion of the error of our path-independent pricing when the underlying is approximated by the Cox, Ross, and Rubinstein (CRR) model. Using this we obtain a corrected model with a convergence of order ⁻³/² to the price of barrier and lookback options in the Black-Scholes model. Our results are supported and illustrated by numerical examples.Infopro Digital Risk (IP)2020-06-02T07:35:03Z2020-06-02T07:35:03Z2019Peer-ReviewedPublished versioninfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articleapplication/pdfLeduc, Guillaume, and Palmer, Kenneth. "Path independence of exotic options and convergence of binomial approximations." Journal of Computational Finance 23, no (2), (2019): 73-102. doi: 10.21314/JCF.2019.372.1755-2850http://hdl.handle.net/11073/1666210.21314/JCF.2019.372.en_UShttps://doi.org/10.21314/JCF.2019.372oai:repository.aus.edu:11073/166622024-08-22T12:01:40Z |
| spellingShingle | Path Independence of Exotic Options and Convergence of Binomial Approximations Leduc, Guillaume Black-Scholes Exotic Barrier Lookback Binomial Path dependence Convergence |
| status_str | publishedVersion |
| title | Path Independence of Exotic Options and Convergence of Binomial Approximations |
| title_full | Path Independence of Exotic Options and Convergence of Binomial Approximations |
| title_fullStr | Path Independence of Exotic Options and Convergence of Binomial Approximations |
| title_full_unstemmed | Path Independence of Exotic Options and Convergence of Binomial Approximations |
| title_short | Path Independence of Exotic Options and Convergence of Binomial Approximations |
| title_sort | Path Independence of Exotic Options and Convergence of Binomial Approximations |
| topic | Black-Scholes Exotic Barrier Lookback Binomial Path dependence Convergence |
| url | http://hdl.handle.net/11073/16662 |