Valoración no lineal de derivados financieros en mercados con iliquidez mediante extensiones del teorema de Feynman-Kac y algoritmos de aprendizaje automático

ilustraciones, diagramas, tablas

Autores:
Moreno Trujillo, John Freddy
Tipo de recurso:
Doctoral thesis
Fecha de publicación:
2024
Institución:
Universidad Nacional de Colombia
Repositorio:
Universidad Nacional de Colombia
Idioma:
spa
OAI Identifier:
oai:repositorio.unal.edu.co:unal/86877
Acceso en línea:
https://repositorio.unal.edu.co/handle/unal/86877
https://repositorio.unal.edu.co/
Palabra clave:
330 - Economía::332 - Economía financiera
510 - Matemáticas::519 - Probabilidades y matemáticas aplicadas
000 - Ciencias de la computación, información y obras generales::006 - Métodos especiales de computación
DERIVADOS FINANCIEROS
OPCIONES (FINANZAS)
TEORIA DEL APRENDIZAJE COMPUTACIONAL
APRENDIZAJE SUPERVISADO (APRENDIZAJE AUTOMATICO)
ECUACIONES DIFERENCIALES NO LINEALES
REDES NEURALES (COMPUTADORES)
Derivative securities
Options (Finance)
Computational learning theory
Supervised learning (Machine learning)
Differential equations, nonlinear
Neural networks (Computer science)
Mercado ilíquido
Valoración de derivados
Ecuaciones diferenciales parciales no lineales
Representación de Feynman-Kac
Redes neuronales artificiales
Illiquid market
Derivative valuation
Nonlinear partial differential equations
Feynman-Kac representation
Artificial neural networks
Rights
openAccess
License
Atribución-NoComercial-SinDerivadas 4.0 Internacional
id UNACIONAL2_4cb43827e83391db4fecbb20420d6513
oai_identifier_str oai:repositorio.unal.edu.co:unal/86877
network_acronym_str UNACIONAL2
network_name_str Universidad Nacional de Colombia
repository_id_str
dc.title.spa.fl_str_mv Valoración no lineal de derivados financieros en mercados con iliquidez mediante extensiones del teorema de Feynman-Kac y algoritmos de aprendizaje automático
dc.title.translated.eng.fl_str_mv Nonlinear valuation of financial derivatives in illiquid markets using extensions of the Feynman-Kac theorem and machine learning algorithms
title Valoración no lineal de derivados financieros en mercados con iliquidez mediante extensiones del teorema de Feynman-Kac y algoritmos de aprendizaje automático
spellingShingle Valoración no lineal de derivados financieros en mercados con iliquidez mediante extensiones del teorema de Feynman-Kac y algoritmos de aprendizaje automático
330 - Economía::332 - Economía financiera
510 - Matemáticas::519 - Probabilidades y matemáticas aplicadas
000 - Ciencias de la computación, información y obras generales::006 - Métodos especiales de computación
DERIVADOS FINANCIEROS
OPCIONES (FINANZAS)
TEORIA DEL APRENDIZAJE COMPUTACIONAL
APRENDIZAJE SUPERVISADO (APRENDIZAJE AUTOMATICO)
ECUACIONES DIFERENCIALES NO LINEALES
REDES NEURALES (COMPUTADORES)
Derivative securities
Options (Finance)
Computational learning theory
Supervised learning (Machine learning)
Differential equations, nonlinear
Neural networks (Computer science)
Mercado ilíquido
Valoración de derivados
Ecuaciones diferenciales parciales no lineales
Representación de Feynman-Kac
Redes neuronales artificiales
Illiquid market
Derivative valuation
Nonlinear partial differential equations
Feynman-Kac representation
Artificial neural networks
title_short Valoración no lineal de derivados financieros en mercados con iliquidez mediante extensiones del teorema de Feynman-Kac y algoritmos de aprendizaje automático
title_full Valoración no lineal de derivados financieros en mercados con iliquidez mediante extensiones del teorema de Feynman-Kac y algoritmos de aprendizaje automático
title_fullStr Valoración no lineal de derivados financieros en mercados con iliquidez mediante extensiones del teorema de Feynman-Kac y algoritmos de aprendizaje automático
title_full_unstemmed Valoración no lineal de derivados financieros en mercados con iliquidez mediante extensiones del teorema de Feynman-Kac y algoritmos de aprendizaje automático
title_sort Valoración no lineal de derivados financieros en mercados con iliquidez mediante extensiones del teorema de Feynman-Kac y algoritmos de aprendizaje automático
dc.creator.fl_str_mv Moreno Trujillo, John Freddy
dc.contributor.advisor.spa.fl_str_mv Hoyos Gómez, Nancy Milena
dc.contributor.author.spa.fl_str_mv Moreno Trujillo, John Freddy
dc.contributor.orcid.spa.fl_str_mv Moreno Trujillo, John Freddy [0000-0002-2772-6931]
dc.contributor.cvlac.spa.fl_str_mv Moreno Trujillo, John Freddy [https://scienti.minciencias.gov.co/cvlac/visualizador/generarCurriculoCv.do?cod_rh=0001028324]
dc.contributor.googlescholar.spa.fl_str_mv Moreno Trujillo, John Freddy [https://scholar.google.com/citations?user=j7aRNrAAAAAJ&hl=es]
dc.subject.ddc.spa.fl_str_mv 330 - Economía::332 - Economía financiera
510 - Matemáticas::519 - Probabilidades y matemáticas aplicadas
000 - Ciencias de la computación, información y obras generales::006 - Métodos especiales de computación
topic 330 - Economía::332 - Economía financiera
510 - Matemáticas::519 - Probabilidades y matemáticas aplicadas
000 - Ciencias de la computación, información y obras generales::006 - Métodos especiales de computación
DERIVADOS FINANCIEROS
OPCIONES (FINANZAS)
TEORIA DEL APRENDIZAJE COMPUTACIONAL
APRENDIZAJE SUPERVISADO (APRENDIZAJE AUTOMATICO)
ECUACIONES DIFERENCIALES NO LINEALES
REDES NEURALES (COMPUTADORES)
Derivative securities
Options (Finance)
Computational learning theory
Supervised learning (Machine learning)
Differential equations, nonlinear
Neural networks (Computer science)
Mercado ilíquido
Valoración de derivados
Ecuaciones diferenciales parciales no lineales
Representación de Feynman-Kac
Redes neuronales artificiales
Illiquid market
Derivative valuation
Nonlinear partial differential equations
Feynman-Kac representation
Artificial neural networks
dc.subject.lemb.spa.fl_str_mv DERIVADOS FINANCIEROS
OPCIONES (FINANZAS)
TEORIA DEL APRENDIZAJE COMPUTACIONAL
APRENDIZAJE SUPERVISADO (APRENDIZAJE AUTOMATICO)
ECUACIONES DIFERENCIALES NO LINEALES
REDES NEURALES (COMPUTADORES)
dc.subject.lemb.eng.fl_str_mv Derivative securities
Options (Finance)
Computational learning theory
Supervised learning (Machine learning)
Differential equations, nonlinear
Neural networks (Computer science)
dc.subject.proposal.spa.fl_str_mv Mercado ilíquido
Valoración de derivados
Ecuaciones diferenciales parciales no lineales
Representación de Feynman-Kac
Redes neuronales artificiales
dc.subject.proposal.eng.fl_str_mv Illiquid market
Derivative valuation
Nonlinear partial differential equations
Feynman-Kac representation
Artificial neural networks
description ilustraciones, diagramas, tablas
publishDate 2024
dc.date.accessioned.none.fl_str_mv 2024-09-30T18:56:11Z
dc.date.available.none.fl_str_mv 2024-09-30T18:56:11Z
dc.date.issued.none.fl_str_mv 2024
dc.type.spa.fl_str_mv Trabajo de grado - Doctorado
dc.type.driver.spa.fl_str_mv info:eu-repo/semantics/doctoralThesis
dc.type.version.spa.fl_str_mv info:eu-repo/semantics/acceptedVersion
dc.type.coar.spa.fl_str_mv http://purl.org/coar/resource_type/c_db06
dc.type.content.spa.fl_str_mv Text
dc.type.redcol.spa.fl_str_mv http://purl.org/redcol/resource_type/TD
format http://purl.org/coar/resource_type/c_db06
status_str acceptedVersion
dc.identifier.uri.none.fl_str_mv https://repositorio.unal.edu.co/handle/unal/86877
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/86877
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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spelling Atribución-NoComercial-SinDerivadas 4.0 Internacionalhttp://creativecommons.org/licenses/by-nc-nd/4.0/info:eu-repo/semantics/openAccesshttp://purl.org/coar/access_right/c_abf2Hoyos Gómez, Nancy Milena12999640324d4aba16dd48e0d34cd393Moreno Trujillo, John Freddy579eacbd7db32a284077f5586cef0d15Moreno Trujillo, John Freddy [0000-0002-2772-6931]Moreno Trujillo, John Freddy [https://scienti.minciencias.gov.co/cvlac/visualizador/generarCurriculoCv.do?cod_rh=0001028324]Moreno Trujillo, John Freddy [https://scholar.google.com/citations?user=j7aRNrAAAAAJ&hl=es]2024-09-30T18:56:11Z2024-09-30T18:56:11Z2024https://repositorio.unal.edu.co/handle/unal/86877Universidad Nacional de ColombiaRepositorio Institucional Universidad Nacional de Colombiahttps://repositorio.unal.edu.co/ilustraciones, diagramas, tablasEn esta investigación se proponen y desarrollan cuatro modelos de mercados financieros ilíquidos, en los cuales se caracteriza la dinámica del precio de los activos riesgosos y la relación emergente entre dicha dinámica y las estrategias de negociación de los agentes. Además, se deducen las correspondientes ecuaciones diferenciales parciales para la valoración de activos contingentes. Específicamente, se presentan: 1. Un modelo de mercado con un factor de iliquidez proporcional al precio del activo; 2. Un modelo en el que la iliquidez es función del precio del activo; 3. Un modelo que incluye iliquidez proporcional, con la presencia de agentes ruidosos (noise traders); 4. Un modelo en el cual la iliquidez es estocástica y está descrita mediante un proceso de reversión a la media de tipo raíz cuadrada. Las ecuaciones de valoración obtenidas son extensiones no lineales de la ecuación diferencial parcial de Black-Scholes, donde la no linealidad resulta del efecto de retroalimentación asociado a la iliquidez del mercado. También se propone, como alternativa para la aproximación a la solución de estas ecuaciones, la aplicación de la extensión del teorema de representación de Feynman-Kac a los casos semi-lineales y completamente no lineales, lo que da lugar a una representación discreta de la solución que puede implementarse de manera eficiente mediante el uso de redes neuronales artificiales (Texto tomado de la fuente).In this research, four models of illiquid financial markets are proposed and developed, characterizing the dynamics of risky asset prices and the emerging relationship between this dynamics and the trading strategies of agents. Additionally, the corresponding partial differential equations for the valuation of contingent assets are deduced. Specifically, the following models are presented: 1. A market model with a liquidity factor proportional to the asset price; 2. A model in which liquidity is a function of the asset price; 3. A model that includes proportional liquidity, with the presence of noise traders; 4. A model in which liquidity is stochastic and described by a mean-reverting square-root process. The resulting valuation equations are nonlinear extensions of the Black-Scholes partial differential equation, where the nonlinearity arises from the feedback effect associated with market illiquidity. As an alternative approach to solving these equations, the application of the extension of the Feynman-Kac representation theorem to semi-linear and fully nonlinear cases is proposed, leading to a discrete representation of the solution that can be efficiently implemented using artificial neural networks.DoctoradoDoctor en Ciencias EconómicasFinanzasx, 121 páginasapplication/pdfspaUniversidad Nacional de ColombiaBogotá - Ciencias Económicas - Doctorado en Ciencias EconómicasFacultad de Ciencias EconómicasBogotá, ColombiaUniversidad Nacional de Colombia - Sede Bogotá330 - Economía::332 - Economía financiera510 - Matemáticas::519 - Probabilidades y matemáticas aplicadas000 - Ciencias de la computación, información y obras generales::006 - Métodos especiales de computaciónDERIVADOS FINANCIEROSOPCIONES (FINANZAS)TEORIA DEL APRENDIZAJE COMPUTACIONALAPRENDIZAJE SUPERVISADO (APRENDIZAJE AUTOMATICO)ECUACIONES DIFERENCIALES NO LINEALESREDES NEURALES (COMPUTADORES)Derivative securitiesOptions (Finance)Computational learning theorySupervised learning (Machine learning)Differential equations, nonlinearNeural networks (Computer science)Mercado ilíquidoValoración de derivadosEcuaciones diferenciales parciales no linealesRepresentación de Feynman-KacRedes neuronales artificialesIlliquid marketDerivative valuationNonlinear partial differential equationsFeynman-Kac representationArtificial neural networksValoración no lineal de derivados financieros en mercados con iliquidez mediante extensiones del teorema de Feynman-Kac y algoritmos de aprendizaje automáticoNonlinear valuation of financial derivatives in illiquid markets using extensions of the Feynman-Kac theorem and machine learning algorithmsTrabajo de grado - Doctoradoinfo:eu-repo/semantics/doctoralThesisinfo:eu-repo/semantics/acceptedVersionhttp://purl.org/coar/resource_type/c_db06Texthttp://purl.org/redcol/resource_type/TDAcharya, V. 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Journal of Futures Markets, 39(11):1471–1485.EstudiantesInvestigadoresMaestrosPúblico generalLICENSElicense.txtlicense.txttext/plain; charset=utf-85879https://repositorio.unal.edu.co/bitstream/unal/86877/1/license.txteb34b1cf90b7e1103fc9dfd26be24b4aMD51ORIGINAL80059098.2024.pdf80059098.2024.pdfTesis de Doctorado en Ciencias Económicasapplication/pdf2004063https://repositorio.unal.edu.co/bitstream/unal/86877/2/80059098.2024.pdfc50d4a86bfab6b110e50d8903474ed09MD52THUMBNAIL80059098.2024.pdf.jpg80059098.2024.pdf.jpgGenerated Thumbnailimage/jpeg5440https://repositorio.unal.edu.co/bitstream/unal/86877/3/80059098.2024.pdf.jpg0b562b23bcd06e4f663a9bc377529abeMD53unal/86877oai:repositorio.unal.edu.co:unal/868772024-09-30 23:18:00.083Repositorio Institucional Universidad Nacional de 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