Valoración de flujos de pagos estocásticos utilizando simulación Monte Carlo con suavizadores y modelos para la estructura temporal de tasas

ilustraciones, gráficas, tablas

Autores:
Rangel Arciniegas, Diego Fernando
Tipo de recurso:
Fecha de publicación:
2021
Institución:
Universidad Nacional de Colombia
Repositorio:
Universidad Nacional de Colombia
Idioma:
spa
OAI Identifier:
oai:repositorio.unal.edu.co:unal/80753
Acceso en línea:
https://repositorio.unal.edu.co/handle/unal/80753
https://repositorio.unal.edu.co/
Palabra clave:
510 - Matemáticas::519 - Probabilidades y matemáticas aplicadas
Estadística
Statistics
Método de Montecarlo
Modelos matemáticos
Anualidades de vida dependientes de fondos
Modelos para estructura temporal de tasas
Nelson-Siegel
Modelo Vasicek
Procesos de difusión
Valores presentes de flujos de caja descontados con tasas variables
Método Monte Carlo
Valoración de pólizas contingentes dependientes de trayectorias
Filtros lineales
Fund-dependent life annuities
Models for interest rates term structure
Nelson-Siegel
Vasicek model
Diffusion processes
Present values of discounted cash flows with variable rates
Monte Carlo method
Valuation of contingent policies dependent on trajectories
Linear filters
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openAccess
License
Reconocimiento 4.0 Internacional
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oai_identifier_str oai:repositorio.unal.edu.co:unal/80753
network_acronym_str UNACIONAL2
network_name_str Universidad Nacional de Colombia
repository_id_str
dc.title.spa.fl_str_mv Valoración de flujos de pagos estocásticos utilizando simulación Monte Carlo con suavizadores y modelos para la estructura temporal de tasas
dc.title.translated.eng.fl_str_mv Valuation of stochastic payment flows using Monte Carlo simulation with smoothing and models for the time structure of rates
title Valoración de flujos de pagos estocásticos utilizando simulación Monte Carlo con suavizadores y modelos para la estructura temporal de tasas
spellingShingle Valoración de flujos de pagos estocásticos utilizando simulación Monte Carlo con suavizadores y modelos para la estructura temporal de tasas
510 - Matemáticas::519 - Probabilidades y matemáticas aplicadas
Estadística
Statistics
Método de Montecarlo
Modelos matemáticos
Anualidades de vida dependientes de fondos
Modelos para estructura temporal de tasas
Nelson-Siegel
Modelo Vasicek
Procesos de difusión
Valores presentes de flujos de caja descontados con tasas variables
Método Monte Carlo
Valoración de pólizas contingentes dependientes de trayectorias
Filtros lineales
Fund-dependent life annuities
Models for interest rates term structure
Nelson-Siegel
Vasicek model
Diffusion processes
Present values of discounted cash flows with variable rates
Monte Carlo method
Valuation of contingent policies dependent on trajectories
Linear filters
title_short Valoración de flujos de pagos estocásticos utilizando simulación Monte Carlo con suavizadores y modelos para la estructura temporal de tasas
title_full Valoración de flujos de pagos estocásticos utilizando simulación Monte Carlo con suavizadores y modelos para la estructura temporal de tasas
title_fullStr Valoración de flujos de pagos estocásticos utilizando simulación Monte Carlo con suavizadores y modelos para la estructura temporal de tasas
title_full_unstemmed Valoración de flujos de pagos estocásticos utilizando simulación Monte Carlo con suavizadores y modelos para la estructura temporal de tasas
title_sort Valoración de flujos de pagos estocásticos utilizando simulación Monte Carlo con suavizadores y modelos para la estructura temporal de tasas
dc.creator.fl_str_mv Rangel Arciniegas, Diego Fernando
dc.contributor.advisor.none.fl_str_mv Giraldo Gómez, Norman Diego
dc.contributor.author.none.fl_str_mv Rangel Arciniegas, Diego Fernando
dc.subject.ddc.spa.fl_str_mv 510 - Matemáticas::519 - Probabilidades y matemáticas aplicadas
topic 510 - Matemáticas::519 - Probabilidades y matemáticas aplicadas
Estadística
Statistics
Método de Montecarlo
Modelos matemáticos
Anualidades de vida dependientes de fondos
Modelos para estructura temporal de tasas
Nelson-Siegel
Modelo Vasicek
Procesos de difusión
Valores presentes de flujos de caja descontados con tasas variables
Método Monte Carlo
Valoración de pólizas contingentes dependientes de trayectorias
Filtros lineales
Fund-dependent life annuities
Models for interest rates term structure
Nelson-Siegel
Vasicek model
Diffusion processes
Present values of discounted cash flows with variable rates
Monte Carlo method
Valuation of contingent policies dependent on trajectories
Linear filters
dc.subject.lemb.none.fl_str_mv Estadística
Statistics
Método de Montecarlo
Modelos matemáticos
dc.subject.proposal.spa.fl_str_mv Anualidades de vida dependientes de fondos
Modelos para estructura temporal de tasas
Nelson-Siegel
Modelo Vasicek
Procesos de difusión
Valores presentes de flujos de caja descontados con tasas variables
Método Monte Carlo
Valoración de pólizas contingentes dependientes de trayectorias
Filtros lineales
dc.subject.proposal.eng.fl_str_mv Fund-dependent life annuities
Models for interest rates term structure
Nelson-Siegel
Vasicek model
Diffusion processes
Present values of discounted cash flows with variable rates
Monte Carlo method
Valuation of contingent policies dependent on trajectories
Linear filters
description ilustraciones, gráficas, tablas
publishDate 2021
dc.date.accessioned.none.fl_str_mv 2021-12-03T15:47:31Z
dc.date.available.none.fl_str_mv 2021-12-03T15:47:31Z
dc.date.issued.none.fl_str_mv 2021-12-01
dc.type.spa.fl_str_mv Trabajo de grado - Maestría
dc.type.driver.spa.fl_str_mv info:eu-repo/semantics/masterThesis
dc.type.version.spa.fl_str_mv info:eu-repo/semantics/acceptedVersion
dc.type.content.spa.fl_str_mv Text
dc.type.redcol.spa.fl_str_mv http://purl.org/redcol/resource_type/TM
status_str acceptedVersion
dc.identifier.uri.none.fl_str_mv https://repositorio.unal.edu.co/handle/unal/80753
dc.identifier.instname.spa.fl_str_mv Universidad Nacional de Colombia
dc.identifier.reponame.spa.fl_str_mv Repositorio Institucional Universidad Nacional de Colombia
dc.identifier.repourl.spa.fl_str_mv https://repositorio.unal.edu.co/
url https://repositorio.unal.edu.co/handle/unal/80753
https://repositorio.unal.edu.co/
identifier_str_mv Universidad Nacional de Colombia
Repositorio Institucional Universidad Nacional de Colombia
dc.language.iso.spa.fl_str_mv spa
language spa
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Bacinello, A. R., Millossovich, P., Olivieri, A. & Pitacco, E. (2011), `Variable annuities: Aunifying valuation approach', Insurance: Mathematics and Economics 49(3), 285-297.
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Biffis, E. (2005), `Affine processes for dynamic mortality and actuarial valuations', Insurance: mathematics and economics 37(3), 443-468.
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Blakey, P. (2006), `The false allure of equity indexed annuities', IEEE Microwave Magazine 7(2), 16-22.
Boulier, J.-F., Huang, S.-J. & Taillard, G. (2001), `Optimal management under stochastic interest rates: the case of a protected de ned contribution pension fund', Insurance: Mathematics and Economics (28), 173-189.
Brouste, A., Fukasawa, M., Hino, H., Iacus, S. M., Kamatani, K., Koike, Y., Masuda, H., Nomura, R., Ogihara, T., Shimuzu, Y., Uchida, M. & Yoshida, N. (2014), `The yuima project: A computational framework for simulation and inference of stochastic di erential equations', Journal of Statistical Software 57(4), 1-51. URL: http://www.jstatsoft.org/v57/i04/
Carriere, J. F. (2004), `Martingale Valuation of Cash Flows for Insurance and Interest Models', North-americal Actuarial Journal 8(3), 150-210.
Chen, D.-f. & Xiang, G. (2003), `Time-risk discount valuation of life contracts', Acta Mathematicae Applicatae Sinica 19(4), 647-662.
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Choe, G. H. (2016), Stochastic analysis for finance with simulations, Springer International Publishing Switzerland.
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De Schepper, A. & Goovaerts, M. (1992), `Some further results on annuities certain with random interest', Insurance: Mathematics and Economics 11(4), 283-290.
Deprez, E. & Schaetzle, T. (1964), `Variable Annuities', 17th International Congress of Actuaries 3(1), 108-120.
Dermoune, A., Djehiche, B. & Rahmania, N. (2008), `A consistent estimator of the smoothing parameter in the hodrick-prescott filter', Journal of the Japan Statistical Society 38(2), 225-241.
Devolder, P. (2016), Finance stochastique, Editions de l'Université de Bruxelles.
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dc.rights.license.spa.fl_str_mv Reconocimiento 4.0 Internacional
dc.rights.uri.spa.fl_str_mv http://creativecommons.org/licenses/by/4.0/
dc.rights.accessrights.spa.fl_str_mv info:eu-repo/semantics/openAccess
rights_invalid_str_mv Reconocimiento 4.0 Internacional
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dc.format.extent.spa.fl_str_mv xvi, 88 páginas
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dc.publisher.spa.fl_str_mv Universidad Nacional de Colombia
dc.publisher.program.spa.fl_str_mv Medellín - Ciencias - Maestría en Ciencias - Estadística
dc.publisher.department.spa.fl_str_mv Escuela de estadística
dc.publisher.faculty.spa.fl_str_mv Facultad de Ciencias
dc.publisher.place.spa.fl_str_mv Medellín, Colombia
dc.publisher.branch.spa.fl_str_mv Universidad Nacional de Colombia - Sede Medellín
institution Universidad Nacional de Colombia
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spelling Reconocimiento 4.0 Internacionalhttp://creativecommons.org/licenses/by/4.0/info:eu-repo/semantics/openAccesshttp://purl.org/coar/access_right/c_abf2Giraldo Gómez, Norman Diego1fe8759b9fc1218bec22a4b4a06a0ff7Rangel Arciniegas, Diego Fernando57610cbdde986266058ff974eb62f8322021-12-03T15:47:31Z2021-12-03T15:47:31Z2021-12-01https://repositorio.unal.edu.co/handle/unal/80753Universidad Nacional de ColombiaRepositorio Institucional Universidad Nacional de Colombiahttps://repositorio.unal.edu.co/ilustraciones, gráficas, tablasLos métodos Monte Carlo son una alternativa utilizada para la valoración de productos financieros. Los productos financieros a los que se refiere este trabajo son las anualidades de las cuales hay varios tipos, que son las rentas vitalicias y los retiros programados y en ambas su expresión para el precio corresponde a una esperanza condicional que depende de dos procesos estocásticos en tiempo continuo: las tasas de interés variables denominadas spot y el rendimiento del fondo, asumidas ambas como proceso de difusión. Esta esperanza puede evaluarse mediante métodos Monte Carlo simulando los respectivos procesos, pero la forma especial del valor esperado permite valorarla también, con cierta restricción, mediante una ecuación diferencial parcial de tipo parabólico con condiciones iniciales y de frontera, conocida como ecuación Feynman-Kac. Esta restricción es que la tasa de interés sea determinística. (Texto tomado de la fuente)Monte Carlo methods are widely used as an alternative for valuation of financial products. The financial products to which this work refers are annuities of which there are several types, which are life annuity and programmed retirement and in both their expression for the price corresponds to a conditional expectation of an expression that depends on two stochastic processes in continuous time: the variable interest rates called spot rate and the fund's performance, both assumed as a di usion process. This expectation can be valued through Monte Carlo methods by simulating the respective processes, but the special form from the expected value also allows to value it, with certain restriction, by a partial di erential equation of parabolic-type with initial and boundary conditions, known as the Feynman-Kac equation. This restriction needs the interest rate to be deterministic.MaestríaMagíster en Ciencias - EstadísticaModelación EstocásticaÁrea Curricular Estadísticaxvi, 88 páginasapplication/pdfspaUniversidad Nacional de ColombiaMedellín - Ciencias - Maestría en Ciencias - EstadísticaEscuela de estadísticaFacultad de CienciasMedellín, ColombiaUniversidad Nacional de Colombia - Sede Medellín510 - Matemáticas::519 - Probabilidades y matemáticas aplicadasEstadísticaStatisticsMétodo de MontecarloModelos matemáticosAnualidades de vida dependientes de fondosModelos para estructura temporal de tasasNelson-SiegelModelo VasicekProcesos de difusiónValores presentes de flujos de caja descontados con tasas variablesMétodo Monte CarloValoración de pólizas contingentes dependientes de trayectoriasFiltros linealesFund-dependent life annuitiesModels for interest rates term structureNelson-SiegelVasicek modelDiffusion processesPresent values of discounted cash flows with variable ratesMonte Carlo methodValuation of contingent policies dependent on trajectoriesLinear filtersValoración de flujos de pagos estocásticos utilizando simulación Monte Carlo con suavizadores y modelos para la estructura temporal de tasasValuation of stochastic payment flows using Monte Carlo simulation with smoothing and models for the time structure of ratesTrabajo de grado - Maestríainfo:eu-repo/semantics/masterThesisinfo:eu-repo/semantics/acceptedVersionTexthttp://purl.org/redcol/resource_type/TMAase, K. K. & Persson, S.-A. (1994), 'Pricing of unit-linked life insurance policies', Scandinavian Actuarial Journal 1994(1), 26-52.Alexandrov, T., Bianconcini, S., Dagum, E. B., Maass, P. & McElroy, T. S. (2012), 'Areview of some modern approaches to the problem of trend extraction', Econometric Reviews 31(6), 593-624.Bacinello, A. R., Millossovich, P., Olivieri, A. & Pitacco, E. (2011), `Variable annuities: Aunifying valuation approach', Insurance: Mathematics and Economics 49(3), 285-297.Berger, A. (1939), Mathematik der Lebensversicherung, Springer-Verlag Wien.Biffis, E. (2005), `Affine processes for dynamic mortality and actuarial valuations', Insurance: mathematics and economics 37(3), 443-468.Blake, D. (2006), Pension Finance, John Wiley and Sons., Chichester.Blake, D., Cairns, A., Coughlan, G., Dowd, K. & MacMinn, R. (2013), `The new life market', Journal of Risk and Insurance 80(3), 501-558.Blakey, P. (2006), `The false allure of equity indexed annuities', IEEE Microwave Magazine 7(2), 16-22.Boulier, J.-F., Huang, S.-J. & Taillard, G. (2001), `Optimal management under stochastic interest rates: the case of a protected de ned contribution pension fund', Insurance: Mathematics and Economics (28), 173-189.Brouste, A., Fukasawa, M., Hino, H., Iacus, S. M., Kamatani, K., Koike, Y., Masuda, H., Nomura, R., Ogihara, T., Shimuzu, Y., Uchida, M. & Yoshida, N. (2014), `The yuima project: A computational framework for simulation and inference of stochastic di erential equations', Journal of Statistical Software 57(4), 1-51. URL: http://www.jstatsoft.org/v57/i04/Carriere, J. F. (2004), `Martingale Valuation of Cash Flows for Insurance and Interest Models', North-americal Actuarial Journal 8(3), 150-210.Chen, D.-f. & Xiang, G. (2003), `Time-risk discount valuation of life contracts', Acta Mathematicae Applicatae Sinica 19(4), 647-662.Chen, R.-R. (1996), Understanding and managing interest rate risks, Vol. 1, World Scientific.Choe, G. H. (2016), Stochastic analysis for finance with simulations, Springer International Publishing Switzerland.Cárdenas-Santamaría, M. (2015), Resolución 3099 de agosto 19 de 2015, Technical report, Ministerio de Hacienda y Crédito Público.De Schepper, A. & Goovaerts, M. (1992), `Some further results on annuities certain with random interest', Insurance: Mathematics and Economics 11(4), 283-290.Deprez, E. & Schaetzle, T. (1964), `Variable Annuities', 17th International Congress of Actuaries 3(1), 108-120.Dermoune, A., Djehiche, B. & Rahmania, N. (2008), `A consistent estimator of the smoothing parameter in the hodrick-prescott filter', Journal of the Japan Statistical Society 38(2), 225-241.Devolder, P. (2016), Finance stochastique, Editions de l'Université de Bruxelles.Dietz, H. M. 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(2020), `The effect of the assumed interest rate and smoothing on variable annuities', ASTIN Bulletin: The Journal of the IAA 50(1), 131-154.EstudiantesInvestigadoresMaestrosLICENSElicense.txtlicense.txttext/plain; charset=utf-84074https://repositorio.unal.edu.co/bitstream/unal/80753/1/license.txt8153f7789df02f0a4c9e079953658ab2MD51ORIGINAL71375862.2021.pdf71375862.2021.pdfTesis de Maestría en Ciencias - Estadísticaapplication/pdf2293157https://repositorio.unal.edu.co/bitstream/unal/80753/2/71375862.2021.pdfc5dd04bcdc3b8982f2553e02967d3599MD52THUMBNAIL71375862.2021.pdf.jpg71375862.2021.pdf.jpgGenerated Thumbnailimage/jpeg5152https://repositorio.unal.edu.co/bitstream/unal/80753/3/71375862.2021.pdf.jpgca4fbc38a27e7c36fbb384c5f711c980MD53unal/80753oai:repositorio.unal.edu.co:unal/807532023-07-31 23:03:56.764Repositorio Institucional Universidad Nacional de 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EVESURBIFBPUiBMQSBTRUNSRVRBUsONQSBHRU5FUkFMLiAqTEEgVEVTSVMgQSBQVUJMSUNBUiBERUJFIFNFUiBMQSBWRVJTScOTTiBGSU5BTCBBUFJPQkFEQS4gCgpBbCBoYWNlciBjbGljIGVuIGVsIHNpZ3VpZW50ZSBib3TDs24sIHVzdGVkIGluZGljYSBxdWUgZXN0w6EgZGUgYWN1ZXJkbyBjb24gZXN0b3MgdMOpcm1pbm9zLiBTaSB0aWVuZSBhbGd1bmEgZHVkYSBzb2JyZSBsYSBsaWNlbmNpYSwgcG9yIGZhdm9yLCBjb250YWN0ZSBjb24gZWwgYWRtaW5pc3RyYWRvciBkZWwgc2lzdGVtYS4KClVOSVZFUlNJREFEIE5BQ0lPTkFMIERFIENPTE9NQklBIC0gw5psdGltYSBtb2RpZmljYWNpw7NuIDE5LzEwLzIwMjEK

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