Binomial tree for option valuation process derived from stochastic autonomous differential equation

This paper proposes a recombination in binomial trees multiplicatively generalized for the autonomous equation, in terms of the initial condition and the product between non-constant jumps up and down the discretized process. A technique is formally presented to find dynamic transition probabilities...

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Autores:
Marín Sánchez, Freddy Hernán
Tipo de recurso:
Fecha de publicación:
2010
Institución:
Universidad EAFIT
Repositorio:
Repositorio EAFIT
Idioma:
spa
OAI Identifier:
oai:repository.eafit.edu.co:10784/14485
Acceso en línea:
http://hdl.handle.net/10784/14485
Palabra clave:
Stochastic Differential Equations
Binomial Trees
Transition Probabilities
Options Valuation
Ecuaciones Diferenciales Estocásticas
Árboles Binomiales
Probabilidades de transición
Valoración de Opciones
Rights
License
Copyright (c) 2010 Freddy Marín-Sánchez
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repository_id_str
spelling Medellín de: Lat: 06 15 00 N degrees minutes Lat: 6.2500 decimal degrees Long: 075 36 00 W degrees minutes Long: -75.6000 decimal degrees2010-12-012019-11-22T19:01:24Z2010-12-012019-11-22T19:01:24Z2256-43141794-9165http://hdl.handle.net/10784/14485This paper proposes a recombination in binomial trees multiplicatively generalized for the autonomous equation, in terms of the initial condition and the product between non-constant jumps up and down the discretized process. A technique is formally presented to find dynamic transition probabilities considering the first two moments of the differential equation solution process, which incorporates the growth factor and volatility in terms of the parameters and the underlying process throughout its branching. Some experimental numerical results of valuation of European options for the log – normal process and for the mean reversion processes with additive noise and proportional noise for different expiration dates are shown.En este trabajo se propone una recombinación en árboles binomiales multiplicativageneralizada para la ecuación autónoma, en términos de la condición inicial y del producto entre saltos no constantes hacia arriba y hacia abajo delproceso discretizado. Se presenta de manera formal una técnica para encontrarlas probabilidades de transición dinámicas considerando los dos primeros momentos del proceso solución de la ecuación diferencial, los cuales incorporanel factor de crecimiento y la volatilidad en términos de los parámetrosy del proceso subyacente a lo largo de su ramificación. Se muestran algunosresultados numéricos experimentales de valoración de opciones Europeas parael proceso log–normal y para los procesos de reversión a la media con ruidoaditivo y ruido proporcional para diferentes fechas de expiración.application/pdfspaUniversidad EAFIThttp://publicaciones.eafit.edu.co/index.php/ingciencia/article/view/337http://publicaciones.eafit.edu.co/index.php/ingciencia/article/view/337Copyright (c) 2010 Freddy Marín-SánchezAcceso abiertohttp://purl.org/coar/access_right/c_abf2instname:Universidad EAFITreponame:Repositorio Institucional Universidad EAFITIngeniería y Ciencia; Vol 6, No 12 (2010)Binomial tree for option valuation process derived from stochastic autonomous differential equationÁrboles binomiales para la valoración de opciones sobre procesos derivados de la ecuación diferencial estocástica autónomaarticleinfo:eu-repo/semantics/articlepublishedVersioninfo:eu-repo/semantics/publishedVersionArtículohttp://purl.org/coar/version/c_970fb48d4fbd8a85http://purl.org/coar/resource_type/c_6501http://purl.org/coar/resource_type/c_2df8fbb1Stochastic Differential EquationsBinomial TreesTransition ProbabilitiesOptions ValuationEcuaciones Diferenciales EstocásticasÁrboles BinomialesProbabilidades de transiciónValoración de OpcionesMarín Sánchez, Freddy HernánUniversidad EAFITIngeniería y Ciencia612145170ing.cienc.ORIGINAL7.pdf7.pdfTexto completo PDFapplication/pdf346965https://repository.eafit.edu.co/bitstreams/ba781f1a-6ad5-4c10-b9a2-4b8e07b4377a/download95b47686447584836a62855f9d4c7ac3MD52articulo.htmlarticulo.htmlTexto completo HTMLtext/html373https://repository.eafit.edu.co/bitstreams/7b83e525-e738-42ac-a937-4690e59c3857/download90d5f867d03dac10e38eb92bf87d6f0eMD53THUMBNAILminaitura-ig_Mesa de trabajo 1.jpgminaitura-ig_Mesa de trabajo 1.jpgimage/jpeg265796https://repository.eafit.edu.co/bitstreams/955db16f-e52f-4e91-990d-da6c88a893d6/downloadda9b21a5c7e00c7f1127cef8e97035e0MD5110784/14485oai:repository.eafit.edu.co:10784/144852020-03-02 22:23:10.27open.accesshttps://repository.eafit.edu.coRepositorio Institucional Universidad EAFITrepositorio@eafit.edu.co
dc.title.eng.fl_str_mv Binomial tree for option valuation process derived from stochastic autonomous differential equation
dc.title.spa.fl_str_mv Árboles binomiales para la valoración de opciones sobre procesos derivados de la ecuación diferencial estocástica autónoma
title Binomial tree for option valuation process derived from stochastic autonomous differential equation
spellingShingle Binomial tree for option valuation process derived from stochastic autonomous differential equation
Stochastic Differential Equations
Binomial Trees
Transition Probabilities
Options Valuation
Ecuaciones Diferenciales Estocásticas
Árboles Binomiales
Probabilidades de transición
Valoración de Opciones
title_short Binomial tree for option valuation process derived from stochastic autonomous differential equation
title_full Binomial tree for option valuation process derived from stochastic autonomous differential equation
title_fullStr Binomial tree for option valuation process derived from stochastic autonomous differential equation
title_full_unstemmed Binomial tree for option valuation process derived from stochastic autonomous differential equation
title_sort Binomial tree for option valuation process derived from stochastic autonomous differential equation
dc.creator.fl_str_mv Marín Sánchez, Freddy Hernán
dc.contributor.author.spa.fl_str_mv Marín Sánchez, Freddy Hernán
dc.contributor.affiliation.spa.fl_str_mv Universidad EAFIT
dc.subject.keyword.eng.fl_str_mv Stochastic Differential Equations
Binomial Trees
Transition Probabilities
Options Valuation
topic Stochastic Differential Equations
Binomial Trees
Transition Probabilities
Options Valuation
Ecuaciones Diferenciales Estocásticas
Árboles Binomiales
Probabilidades de transición
Valoración de Opciones
dc.subject.keyword.spa.fl_str_mv Ecuaciones Diferenciales Estocásticas
Árboles Binomiales
Probabilidades de transición
Valoración de Opciones
description This paper proposes a recombination in binomial trees multiplicatively generalized for the autonomous equation, in terms of the initial condition and the product between non-constant jumps up and down the discretized process. A technique is formally presented to find dynamic transition probabilities considering the first two moments of the differential equation solution process, which incorporates the growth factor and volatility in terms of the parameters and the underlying process throughout its branching. Some experimental numerical results of valuation of European options for the log – normal process and for the mean reversion processes with additive noise and proportional noise for different expiration dates are shown.
publishDate 2010
dc.date.issued.none.fl_str_mv 2010-12-01
dc.date.available.none.fl_str_mv 2019-11-22T19:01:24Z
dc.date.accessioned.none.fl_str_mv 2019-11-22T19:01:24Z
dc.date.none.fl_str_mv 2010-12-01
dc.type.eng.fl_str_mv article
info:eu-repo/semantics/article
publishedVersion
info:eu-repo/semantics/publishedVersion
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dc.type.coar.fl_str_mv http://purl.org/coar/resource_type/c_6501
http://purl.org/coar/resource_type/c_2df8fbb1
dc.type.local.spa.fl_str_mv Artículo
status_str publishedVersion
dc.identifier.issn.none.fl_str_mv 2256-4314
1794-9165
dc.identifier.uri.none.fl_str_mv http://hdl.handle.net/10784/14485
identifier_str_mv 2256-4314
1794-9165
url http://hdl.handle.net/10784/14485
dc.language.iso.spa.fl_str_mv spa
language spa
dc.relation.isversionof.none.fl_str_mv http://publicaciones.eafit.edu.co/index.php/ingciencia/article/view/337
dc.relation.uri.none.fl_str_mv http://publicaciones.eafit.edu.co/index.php/ingciencia/article/view/337
dc.rights.eng.fl_str_mv Copyright (c) 2010 Freddy Marín-Sánchez
dc.rights.coar.fl_str_mv http://purl.org/coar/access_right/c_abf2
dc.rights.local.spa.fl_str_mv Acceso abierto
rights_invalid_str_mv Copyright (c) 2010 Freddy Marín-Sánchez
Acceso abierto
http://purl.org/coar/access_right/c_abf2
dc.format.none.fl_str_mv application/pdf
dc.coverage.spatial.eng.fl_str_mv Medellín de: Lat: 06 15 00 N degrees minutes Lat: 6.2500 decimal degrees Long: 075 36 00 W degrees minutes Long: -75.6000 decimal degrees
dc.publisher.spa.fl_str_mv Universidad EAFIT
dc.source.none.fl_str_mv instname:Universidad EAFIT
reponame:Repositorio Institucional Universidad EAFIT
dc.source.spa.fl_str_mv Ingeniería y Ciencia; Vol 6, No 12 (2010)
instname_str Universidad EAFIT
institution Universidad EAFIT
reponame_str Repositorio Institucional Universidad EAFIT
collection Repositorio Institucional Universidad EAFIT
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