Least squares Monte Carlo methods in stochastic Volterra rough volatility models
Autor(a) principal: | |
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Data de Publicação: | 2021 |
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/10400.5/21324 |
Resumo: | In stochastic Volterra rough volatility models, the volatility follows a truncated Brownian semi-stationary process with stochastic vol-of-vol. Recently, efficient VIX pricing Monte Carlo methods have been proposed for the case where the vol-of-vol is Markovian and independent of the volatility. Following recent empirical data, we discuss the VIX option pricing problem for a generalized framework of these models, where the vol-of-vol may depend on the volatility and/or not be Markovian. In such a setting, the aforementioned Monte Carlo methods are not valid. Moreover, the classical least squares Monte Carlo faces exponentially increasing complexity with the number of grid time steps, whilst the nested Monte Carlo method requires a prohibitive number of simulations. By exploring the infinite dimensional Markovian representation of these models, we device a scalable least squares Monte Carlo for VIX option pricing. We apply our method firstly under the independence assumption for benchmarks, and then to the generalized framework. We also discuss the rough vol-of-vol setting, where Markovianity of the vol-of-vol is not present. We present simulations and benchmarks to establish the efficiency of our method. |
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Least squares Monte Carlo methods in stochastic Volterra rough volatility modelsVIXrough volatilitystochastic Volterra modelsleast squares Monte Carlovolatility of volatilityIn stochastic Volterra rough volatility models, the volatility follows a truncated Brownian semi-stationary process with stochastic vol-of-vol. Recently, efficient VIX pricing Monte Carlo methods have been proposed for the case where the vol-of-vol is Markovian and independent of the volatility. Following recent empirical data, we discuss the VIX option pricing problem for a generalized framework of these models, where the vol-of-vol may depend on the volatility and/or not be Markovian. In such a setting, the aforementioned Monte Carlo methods are not valid. Moreover, the classical least squares Monte Carlo faces exponentially increasing complexity with the number of grid time steps, whilst the nested Monte Carlo method requires a prohibitive number of simulations. By exploring the infinite dimensional Markovian representation of these models, we device a scalable least squares Monte Carlo for VIX option pricing. We apply our method firstly under the independence assumption for benchmarks, and then to the generalized framework. We also discuss the rough vol-of-vol setting, where Markovianity of the vol-of-vol is not present. We present simulations and benchmarks to establish the efficiency of our method.ISEG - REM - Research in Economics and MathematicsRepositório da Universidade de LisboaGuerreiro, HenriqueGuerra, João2021-05-20T13:14:39Z2021-052021-05-01T00:00:00Zinfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articleapplication/pdfhttp://hdl.handle.net/10400.5/21324engGuerreiro, Henrique e João Guerra (2021). "Least squares Monte Carlo methods in stochastic Volterra rough volatility models". Instituto Superior de Economia e Gestão – REM Working paper nº 0176 – 20212184-108Xinfo: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:RCAAP2023-03-06T14:50:45Zoai:www.repository.utl.pt:10400.5/21324Portal AgregadorONGhttps://www.rcaap.pt/oai/openaireopendoar:71602024-03-19T17:05:55.809621Repositório 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 |
Least squares Monte Carlo methods in stochastic Volterra rough volatility models |
title |
Least squares Monte Carlo methods in stochastic Volterra rough volatility models |
spellingShingle |
Least squares Monte Carlo methods in stochastic Volterra rough volatility models Guerreiro, Henrique VIX rough volatility stochastic Volterra models least squares Monte Carlo volatility of volatility |
title_short |
Least squares Monte Carlo methods in stochastic Volterra rough volatility models |
title_full |
Least squares Monte Carlo methods in stochastic Volterra rough volatility models |
title_fullStr |
Least squares Monte Carlo methods in stochastic Volterra rough volatility models |
title_full_unstemmed |
Least squares Monte Carlo methods in stochastic Volterra rough volatility models |
title_sort |
Least squares Monte Carlo methods in stochastic Volterra rough volatility models |
author |
Guerreiro, Henrique |
author_facet |
Guerreiro, Henrique Guerra, João |
author_role |
author |
author2 |
Guerra, João |
author2_role |
author |
dc.contributor.none.fl_str_mv |
Repositório da Universidade de Lisboa |
dc.contributor.author.fl_str_mv |
Guerreiro, Henrique Guerra, João |
dc.subject.por.fl_str_mv |
VIX rough volatility stochastic Volterra models least squares Monte Carlo volatility of volatility |
topic |
VIX rough volatility stochastic Volterra models least squares Monte Carlo volatility of volatility |
description |
In stochastic Volterra rough volatility models, the volatility follows a truncated Brownian semi-stationary process with stochastic vol-of-vol. Recently, efficient VIX pricing Monte Carlo methods have been proposed for the case where the vol-of-vol is Markovian and independent of the volatility. Following recent empirical data, we discuss the VIX option pricing problem for a generalized framework of these models, where the vol-of-vol may depend on the volatility and/or not be Markovian. In such a setting, the aforementioned Monte Carlo methods are not valid. Moreover, the classical least squares Monte Carlo faces exponentially increasing complexity with the number of grid time steps, whilst the nested Monte Carlo method requires a prohibitive number of simulations. By exploring the infinite dimensional Markovian representation of these models, we device a scalable least squares Monte Carlo for VIX option pricing. We apply our method firstly under the independence assumption for benchmarks, and then to the generalized framework. We also discuss the rough vol-of-vol setting, where Markovianity of the vol-of-vol is not present. We present simulations and benchmarks to establish the efficiency of our method. |
publishDate |
2021 |
dc.date.none.fl_str_mv |
2021-05-20T13:14:39Z 2021-05 2021-05-01T00:00:00Z |
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/10400.5/21324 |
url |
http://hdl.handle.net/10400.5/21324 |
dc.language.iso.fl_str_mv |
eng |
language |
eng |
dc.relation.none.fl_str_mv |
Guerreiro, Henrique e João Guerra (2021). "Least squares Monte Carlo methods in stochastic Volterra rough volatility models". Instituto Superior de Economia e Gestão – REM Working paper nº 0176 – 2021 2184-108X |
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 - REM - Research in Economics and Mathematics |
publisher.none.fl_str_mv |
ISEG - REM - Research in Economics and Mathematics |
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 |
instname_str |
Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informação |
instacron_str |
RCAAP |
institution |
RCAAP |
reponame_str |
Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) |
collection |
Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) |
repository.name.fl_str_mv |
Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) - Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informação |
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1799131152005464064 |