Convexity adjustments for ATS models
Autor(a) principal: | |
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Data de Publicação: | 2008 |
Outros Autores: | |
Tipo de documento: | Artigo |
Idioma: | eng |
Título da fonte: | Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) |
Texto Completo: | http://hdl.handle.net/10400.5/2565 |
Resumo: | Practitioners are used to value a broad class of exotic interest rate derivatives simply by adjusting for what is known as convexity adjustments (or convexity corrections). We start by exploiting the relations between various interest rate models and their connections to measure changes. As a result we classify convexity adjustments into forward adjustments and swaps adjustments. We, then, focus on affine term structure (ATS) models and, in this context, conjecture convexity adjustments should be related of affine functionals. In the case of forward ad¬justments, we show how to obtain exact formulas. Concretely for LIBOR in arrears (LIA) contracts, we derive the system of Riccatti ODE-s one needs to compute to obtain the exact adjustment. Based upon the ideas of Schrager and Pelsser (2006) we are also able to derive general swap adjustments useful, in particular, when dealing with constant maturity swaps (CMS). Our approach bypasses the need for Taylor approximations or unrealistic assumptions. They include exact convexity adjustments previously derived, such as the adjustments associated with Gaussian models, but are far more general as they provide solutions for the entire ATS class of models. |
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Convexity adjustments for ATS modelsAffine Term StructureConvexity AdjustmentsCMSLIBOR in ArrearsPractitioners are used to value a broad class of exotic interest rate derivatives simply by adjusting for what is known as convexity adjustments (or convexity corrections). We start by exploiting the relations between various interest rate models and their connections to measure changes. As a result we classify convexity adjustments into forward adjustments and swaps adjustments. We, then, focus on affine term structure (ATS) models and, in this context, conjecture convexity adjustments should be related of affine functionals. In the case of forward ad¬justments, we show how to obtain exact formulas. Concretely for LIBOR in arrears (LIA) contracts, we derive the system of Riccatti ODE-s one needs to compute to obtain the exact adjustment. Based upon the ideas of Schrager and Pelsser (2006) we are also able to derive general swap adjustments useful, in particular, when dealing with constant maturity swaps (CMS). Our approach bypasses the need for Taylor approximations or unrealistic assumptions. They include exact convexity adjustments previously derived, such as the adjustments associated with Gaussian models, but are far more general as they provide solutions for the entire ATS class of models.Financial support of FCT under grant PTDC/MAT/64838/2006 and Jan Wallander's FoundationISEG - Departamento de GestãoRepositório da Universidade de LisboaGaspar, Raquel M.Murgoci, Agatha2010-11-24T12:36:25Z20082008-01-01T00:00:00Zinfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articleapplication/pdfhttp://hdl.handle.net/10400.5/2565engGaspar, Raquel M. e Agatha Murgoci. 2008. "Convexity adjustments for ATS models". Instituto Superior de Economia e Gestão . Documento de trabalho – ADVANCE Working paper nº 9-08info:eu-repo/semantics/openAccessreponame:Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)instname:Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informaçãoinstacron:RCAAP2023-03-06T14:33:44Zoai:www.repository.utl.pt:10400.5/2565Portal AgregadorONGhttps://www.rcaap.pt/oai/openaireopendoar:71602024-03-19T16:50:33.459213Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) - Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informaçãofalse |
dc.title.none.fl_str_mv |
Convexity adjustments for ATS models |
title |
Convexity adjustments for ATS models |
spellingShingle |
Convexity adjustments for ATS models Gaspar, Raquel M. Affine Term Structure Convexity Adjustments CMS LIBOR in Arrears |
title_short |
Convexity adjustments for ATS models |
title_full |
Convexity adjustments for ATS models |
title_fullStr |
Convexity adjustments for ATS models |
title_full_unstemmed |
Convexity adjustments for ATS models |
title_sort |
Convexity adjustments for ATS models |
author |
Gaspar, Raquel M. |
author_facet |
Gaspar, Raquel M. Murgoci, Agatha |
author_role |
author |
author2 |
Murgoci, Agatha |
author2_role |
author |
dc.contributor.none.fl_str_mv |
Repositório da Universidade de Lisboa |
dc.contributor.author.fl_str_mv |
Gaspar, Raquel M. Murgoci, Agatha |
dc.subject.por.fl_str_mv |
Affine Term Structure Convexity Adjustments CMS LIBOR in Arrears |
topic |
Affine Term Structure Convexity Adjustments CMS LIBOR in Arrears |
description |
Practitioners are used to value a broad class of exotic interest rate derivatives simply by adjusting for what is known as convexity adjustments (or convexity corrections). We start by exploiting the relations between various interest rate models and their connections to measure changes. As a result we classify convexity adjustments into forward adjustments and swaps adjustments. We, then, focus on affine term structure (ATS) models and, in this context, conjecture convexity adjustments should be related of affine functionals. In the case of forward ad¬justments, we show how to obtain exact formulas. Concretely for LIBOR in arrears (LIA) contracts, we derive the system of Riccatti ODE-s one needs to compute to obtain the exact adjustment. Based upon the ideas of Schrager and Pelsser (2006) we are also able to derive general swap adjustments useful, in particular, when dealing with constant maturity swaps (CMS). Our approach bypasses the need for Taylor approximations or unrealistic assumptions. They include exact convexity adjustments previously derived, such as the adjustments associated with Gaussian models, but are far more general as they provide solutions for the entire ATS class of models. |
publishDate |
2008 |
dc.date.none.fl_str_mv |
2008 2008-01-01T00:00:00Z 2010-11-24T12:36:25Z |
dc.type.status.fl_str_mv |
info:eu-repo/semantics/publishedVersion |
dc.type.driver.fl_str_mv |
info:eu-repo/semantics/article |
format |
article |
status_str |
publishedVersion |
dc.identifier.uri.fl_str_mv |
http://hdl.handle.net/10400.5/2565 |
url |
http://hdl.handle.net/10400.5/2565 |
dc.language.iso.fl_str_mv |
eng |
language |
eng |
dc.relation.none.fl_str_mv |
Gaspar, Raquel M. e Agatha Murgoci. 2008. "Convexity adjustments for ATS models". Instituto Superior de Economia e Gestão . Documento de trabalho – ADVANCE Working paper nº 9-08 |
dc.rights.driver.fl_str_mv |
info:eu-repo/semantics/openAccess |
eu_rights_str_mv |
openAccess |
dc.format.none.fl_str_mv |
application/pdf |
dc.publisher.none.fl_str_mv |
ISEG - Departamento de Gestão |
publisher.none.fl_str_mv |
ISEG - Departamento de Gestão |
dc.source.none.fl_str_mv |
reponame:Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) instname:Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informação instacron:RCAAP |
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Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informação |
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RCAAP |
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RCAAP |
reponame_str |
Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) |
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Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) |
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Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) - Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informação |
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