Essays on bivariate option pricing via copula and heteroscedasticity models: a classical and bayesian approach
Autor(a) principal: | |
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Data de Publicação: | 2019 |
Tipo de documento: | Dissertação |
Idioma: | eng |
Título da fonte: | Repositório Institucional da UFSCAR |
Texto Completo: | https://repositorio.ufscar.br/handle/ufscar/11246 |
Resumo: | This dissertation is composed of two main and independents essays, but complementary. In the first one, we discuss the option price under a bayesian perspective. This essay aims to price and analyze the fair price behavior of the call-on-max (bivariate) option considering marginal heteroscedastic models with dependence structure modeled via copulas. Concerning inference, we adopt a Bayesian perspective and computationally intensive methods based on Monte Carlo simulations via Markov Chain (MCMC). A simulation study examines the bias and the root mean squared errors of the posterior means for the parameters. Real stocks prices of Brazilian banks illustrate the approach. For the proposed method is verified the effects of strike and dependence structure on the fair price of the option. The results show that the prices obtained by our heteroscedastic model approach and copulas differ substantially from the prices obtained by the model derived from Black and Scholes. Empirical results are presented to argue the advantages of our strategy. In the second chapter, we consider the GARCH-in-mean models with asymmetric variance specifications to model the volatility of the assets-objects under the risk-neutral dynamics. Moreover, the copula functions model the joint distribution, with the objective of capturing non-linear, linear and tails associations between the assets. We aim to provide a methodology to realize a more realistic pricing option. To illustrate the methodology, we use stocks from two Brazilian companies, where our the modeling offered a proper fitting. Confronting the results obtained with the classic model, which is an extension of the Black and Scholes model, we note that considering constant volatility over time underpricing the options, especially in-the-money options. |
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Lopes, Lucas PereiraCancho, Vicente Garibayhttp://lattes.cnpq.br/3503233632044163http://lattes.cnpq.br/59689998046231982019-04-17T11:21:41Z2019-04-17T11:21:41Z2019-02-15LOPES, Lucas Pereira. Essays on bivariate option pricing via copula and heteroscedasticity models: a classical and bayesian approach. 2019. Dissertação (Mestrado em Estatística) – Universidade Federal de São Carlos, São Carlos, 2019. Disponível em: https://repositorio.ufscar.br/handle/ufscar/11246.https://repositorio.ufscar.br/handle/ufscar/11246This dissertation is composed of two main and independents essays, but complementary. In the first one, we discuss the option price under a bayesian perspective. This essay aims to price and analyze the fair price behavior of the call-on-max (bivariate) option considering marginal heteroscedastic models with dependence structure modeled via copulas. Concerning inference, we adopt a Bayesian perspective and computationally intensive methods based on Monte Carlo simulations via Markov Chain (MCMC). A simulation study examines the bias and the root mean squared errors of the posterior means for the parameters. Real stocks prices of Brazilian banks illustrate the approach. For the proposed method is verified the effects of strike and dependence structure on the fair price of the option. The results show that the prices obtained by our heteroscedastic model approach and copulas differ substantially from the prices obtained by the model derived from Black and Scholes. Empirical results are presented to argue the advantages of our strategy. In the second chapter, we consider the GARCH-in-mean models with asymmetric variance specifications to model the volatility of the assets-objects under the risk-neutral dynamics. Moreover, the copula functions model the joint distribution, with the objective of capturing non-linear, linear and tails associations between the assets. We aim to provide a methodology to realize a more realistic pricing option. To illustrate the methodology, we use stocks from two Brazilian companies, where our the modeling offered a proper fitting. Confronting the results obtained with the classic model, which is an extension of the Black and Scholes model, we note that considering constant volatility over time underpricing the options, especially in-the-money options.Essa dissertação é composta por dois principais ensaios independentes e complementares. No primeiro discutimos a precificação de opções bivariadas sob uma perspectiva bayesiana. Neste ensaio o principal objetivo foi precificar e analizar o preço justo da opção bivariada call-on-max considerando modelos heterocedásticos para as marginais e a modelagem de dependência realizada por funções cópulas. Para a inferência, adotamos o método computacionalmente intensivo baseado em simulações Monte Carlo via Cadeia de Markov (MCMC). Um estudo de simulação examinou o viés e o erro quadrático médio dos parâmetros a posteriori. Para a ilustração da abordagem, foram utilizados preços de ações de bancos Brasileiros. Além disso, foi verificado o efeito do strike e da estrutura de dependência nos preços das opções. Os resultados mostraram que os preços obtidos pelo método utilizado difere substancialmente dos obtidos pelo modelo clássico derivado de Black e Scholes. No segundo capítulo, consideramos os modelos GARCH-in-mean com especificações assimétricas para a variância com o objetivo de acomodar as características da volatilidade dos ativos-objetos sob uma perspectiva da dinâmica do risco-neutro. Além do mais, as funções cópulas foram utilizadas para capturar as possíveis estruturas de dependência linear, não-linear e caudais entre os ativos. Para ilustrar a metodologia, utilizamos dados de duas companhias Brasileiras. Confrontando os resultados obtidos com o modelo clássico extendido de Black e Scholes, notamos que a premissa de volatilidade constante sub-precifica as opções bivariadas, especialmente dentro-do-dinheiro.Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)CAPES: 1689441engUniversidade Federal de São CarlosCâmpus São CarlosPrograma Interinstitucional de Pós-Graduação em Estatística - PIPGEsUFSCarPrecificaçãoOpçõesModelos heterocedásticosCópulaInferência bayesianaPricingOptionHeterocedastic modelCopulaBayesian inferenceCIENCIAS EXATAS E DA TERRA::PROBABILIDADE E ESTATISTICAEssays on bivariate option pricing via copula and heteroscedasticity models: a classical and bayesian approachEnsaios sobre precificação de opções bivariadas via cópulas e modelos heterocedásticos: abordagem clássica e bayesianainfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/masterThesisOnlineinfo:eu-repo/semantics/openAccessreponame:Repositório Institucional da UFSCARinstname:Universidade Federal de São Carlos (UFSCAR)instacron:UFSCARORIGINALDissertação - Lucas Pereira Lopes.pdfDissertação - Lucas Pereira Lopes.pdfDissertaçãoapplication/pdf3818825https://{{ getenv "DSPACE_HOST" "repositorio.ufscar.br" }}/bitstream/ufscar/11246/1/Disserta%c3%a7%c3%a3o%20-%20Lucas%20Pereira%20Lopes.pdf2c4c5444b424e1f25e329b54c376f217MD51LICENSElicense.txtlicense.txttext/plain; charset=utf-81957https://{{ getenv "DSPACE_HOST" "repositorio.ufscar.br" }}/bitstream/ufscar/11246/5/license.txtae0398b6f8b235e40ad82cba6c50031dMD55TEXTDissertação - Lucas Pereira Lopes.pdf.txtDissertação - Lucas Pereira Lopes.pdf.txtExtracted texttext/plain156914https://{{ getenv "DSPACE_HOST" "repositorio.ufscar.br" }}/bitstream/ufscar/11246/6/Disserta%c3%a7%c3%a3o%20-%20Lucas%20Pereira%20Lopes.pdf.txt68077711a7759b6f52fd1b9bae9af3f8MD56THUMBNAILDissertação - Lucas Pereira Lopes.pdf.jpgDissertação - Lucas Pereira Lopes.pdf.jpgIM Thumbnailimage/jpeg12346https://{{ getenv "DSPACE_HOST" "repositorio.ufscar.br" }}/bitstream/ufscar/11246/7/Disserta%c3%a7%c3%a3o%20-%20Lucas%20Pereira%20Lopes.pdf.jpgabad842d780d67e9fb6e4cf48ab69840MD57ufscar/112462019-09-11 03:44:46.945oai:repositorio.ufscar.br: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Repositório InstitucionalPUBhttps://repositorio.ufscar.br/oai/requestopendoar:43222019-09-11T03:44:46Repositório Institucional da UFSCAR - Universidade Federal de São Carlos (UFSCAR)false |
dc.title.eng.fl_str_mv |
Essays on bivariate option pricing via copula and heteroscedasticity models: a classical and bayesian approach |
dc.title.alternative.por.fl_str_mv |
Ensaios sobre precificação de opções bivariadas via cópulas e modelos heterocedásticos: abordagem clássica e bayesiana |
title |
Essays on bivariate option pricing via copula and heteroscedasticity models: a classical and bayesian approach |
spellingShingle |
Essays on bivariate option pricing via copula and heteroscedasticity models: a classical and bayesian approach Lopes, Lucas Pereira Precificação Opções Modelos heterocedásticos Cópula Inferência bayesiana Pricing Option Heterocedastic model Copula Bayesian inference CIENCIAS EXATAS E DA TERRA::PROBABILIDADE E ESTATISTICA |
title_short |
Essays on bivariate option pricing via copula and heteroscedasticity models: a classical and bayesian approach |
title_full |
Essays on bivariate option pricing via copula and heteroscedasticity models: a classical and bayesian approach |
title_fullStr |
Essays on bivariate option pricing via copula and heteroscedasticity models: a classical and bayesian approach |
title_full_unstemmed |
Essays on bivariate option pricing via copula and heteroscedasticity models: a classical and bayesian approach |
title_sort |
Essays on bivariate option pricing via copula and heteroscedasticity models: a classical and bayesian approach |
author |
Lopes, Lucas Pereira |
author_facet |
Lopes, Lucas Pereira |
author_role |
author |
dc.contributor.authorlattes.por.fl_str_mv |
http://lattes.cnpq.br/5968999804623198 |
dc.contributor.author.fl_str_mv |
Lopes, Lucas Pereira |
dc.contributor.advisor1.fl_str_mv |
Cancho, Vicente Garibay |
dc.contributor.advisor1Lattes.fl_str_mv |
http://lattes.cnpq.br/3503233632044163 |
contributor_str_mv |
Cancho, Vicente Garibay |
dc.subject.por.fl_str_mv |
Precificação Opções Modelos heterocedásticos Cópula Inferência bayesiana |
topic |
Precificação Opções Modelos heterocedásticos Cópula Inferência bayesiana Pricing Option Heterocedastic model Copula Bayesian inference CIENCIAS EXATAS E DA TERRA::PROBABILIDADE E ESTATISTICA |
dc.subject.eng.fl_str_mv |
Pricing Option Heterocedastic model Copula Bayesian inference |
dc.subject.cnpq.fl_str_mv |
CIENCIAS EXATAS E DA TERRA::PROBABILIDADE E ESTATISTICA |
description |
This dissertation is composed of two main and independents essays, but complementary. In the first one, we discuss the option price under a bayesian perspective. This essay aims to price and analyze the fair price behavior of the call-on-max (bivariate) option considering marginal heteroscedastic models with dependence structure modeled via copulas. Concerning inference, we adopt a Bayesian perspective and computationally intensive methods based on Monte Carlo simulations via Markov Chain (MCMC). A simulation study examines the bias and the root mean squared errors of the posterior means for the parameters. Real stocks prices of Brazilian banks illustrate the approach. For the proposed method is verified the effects of strike and dependence structure on the fair price of the option. The results show that the prices obtained by our heteroscedastic model approach and copulas differ substantially from the prices obtained by the model derived from Black and Scholes. Empirical results are presented to argue the advantages of our strategy. In the second chapter, we consider the GARCH-in-mean models with asymmetric variance specifications to model the volatility of the assets-objects under the risk-neutral dynamics. Moreover, the copula functions model the joint distribution, with the objective of capturing non-linear, linear and tails associations between the assets. We aim to provide a methodology to realize a more realistic pricing option. To illustrate the methodology, we use stocks from two Brazilian companies, where our the modeling offered a proper fitting. Confronting the results obtained with the classic model, which is an extension of the Black and Scholes model, we note that considering constant volatility over time underpricing the options, especially in-the-money options. |
publishDate |
2019 |
dc.date.accessioned.fl_str_mv |
2019-04-17T11:21:41Z |
dc.date.available.fl_str_mv |
2019-04-17T11:21:41Z |
dc.date.issued.fl_str_mv |
2019-02-15 |
dc.type.status.fl_str_mv |
info:eu-repo/semantics/publishedVersion |
dc.type.driver.fl_str_mv |
info:eu-repo/semantics/masterThesis |
format |
masterThesis |
status_str |
publishedVersion |
dc.identifier.citation.fl_str_mv |
LOPES, Lucas Pereira. Essays on bivariate option pricing via copula and heteroscedasticity models: a classical and bayesian approach. 2019. Dissertação (Mestrado em Estatística) – Universidade Federal de São Carlos, São Carlos, 2019. Disponível em: https://repositorio.ufscar.br/handle/ufscar/11246. |
dc.identifier.uri.fl_str_mv |
https://repositorio.ufscar.br/handle/ufscar/11246 |
identifier_str_mv |
LOPES, Lucas Pereira. Essays on bivariate option pricing via copula and heteroscedasticity models: a classical and bayesian approach. 2019. Dissertação (Mestrado em Estatística) – Universidade Federal de São Carlos, São Carlos, 2019. Disponível em: https://repositorio.ufscar.br/handle/ufscar/11246. |
url |
https://repositorio.ufscar.br/handle/ufscar/11246 |
dc.language.iso.fl_str_mv |
eng |
language |
eng |
dc.rights.driver.fl_str_mv |
info:eu-repo/semantics/openAccess |
eu_rights_str_mv |
openAccess |
dc.publisher.none.fl_str_mv |
Universidade Federal de São Carlos Câmpus São Carlos |
dc.publisher.program.fl_str_mv |
Programa Interinstitucional de Pós-Graduação em Estatística - PIPGEs |
dc.publisher.initials.fl_str_mv |
UFSCar |
publisher.none.fl_str_mv |
Universidade Federal de São Carlos Câmpus São Carlos |
dc.source.none.fl_str_mv |
reponame:Repositório Institucional da UFSCAR instname:Universidade Federal de São Carlos (UFSCAR) instacron:UFSCAR |
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Universidade Federal de São Carlos (UFSCAR) |
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UFSCAR |
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UFSCAR |
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Repositório Institucional da UFSCAR |
collection |
Repositório Institucional da UFSCAR |
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