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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التفاصيل البيبلوغرافية
المؤلف الرئيسي: Leduc, Guillaume (author)
مؤلفون آخرون: Palmer, Kenneth J. (author)
التنسيق: article
منشور في: 2019
الموضوعات:
الوصول للمادة أونلاين:http://hdl.handle.net/11073/16662
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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.
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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