Super-replication under gamma constraints: An application to forward start options
Esta tesis sirve como una introducción al problema y a los resultados de la super-replicación de derivados financieros con restricciones en gamma, tal como lo presentan Soner y Touzi. En el tercer capítulo se presenta una extensión leve e inmediata del resultado de Soner y Touzi para incluir el desc...
- Autores:
-
Arango Arango, Sergio
- Tipo de recurso:
- Trabajo de grado de pregrado
- Fecha de publicación:
- 2025
- Institución:
- Universidad de los Andes
- Repositorio:
- Séneca: repositorio Uniandes
- Idioma:
- eng
- OAI Identifier:
- oai:repositorio.uniandes.edu.co:1992/75769
- Acceso en línea:
- https://hdl.handle.net/1992/75769
- Palabra clave:
- Derivados
Gamma
Black-Scholes
Soner
Touzi
Matemáticas
- Rights
- openAccess
- License
- Attribution-NonCommercial-NoDerivatives 4.0 International
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Super-replication under gamma constraints: An application to forward start options |
| title |
Super-replication under gamma constraints: An application to forward start options |
| spellingShingle |
Super-replication under gamma constraints: An application to forward start options Derivados Gamma Black-Scholes Soner Touzi Matemáticas |
| title_short |
Super-replication under gamma constraints: An application to forward start options |
| title_full |
Super-replication under gamma constraints: An application to forward start options |
| title_fullStr |
Super-replication under gamma constraints: An application to forward start options |
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Super-replication under gamma constraints: An application to forward start options |
| title_sort |
Super-replication under gamma constraints: An application to forward start options |
| dc.creator.fl_str_mv |
Arango Arango, Sergio |
| dc.contributor.advisor.none.fl_str_mv |
Jara Pinzón, Diego Junca Peláez, Mauricio José |
| dc.contributor.author.none.fl_str_mv |
Arango Arango, Sergio |
| dc.contributor.jury.none.fl_str_mv |
Hernández, Camilo |
| dc.subject.keyword.spa.fl_str_mv |
Derivados |
| topic |
Derivados Gamma Black-Scholes Soner Touzi Matemáticas |
| dc.subject.keyword.none.fl_str_mv |
Gamma Black-Scholes Soner Touzi |
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Matemáticas |
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Esta tesis sirve como una introducción al problema y a los resultados de la super-replicación de derivados financieros con restricciones en gamma, tal como lo presentan Soner y Touzi. En el tercer capítulo se presenta una extensión leve e inmediata del resultado de Soner y Touzi para incluir el descuento con una tasa fija y determinista bajo un factor de descuento continuo. El objeto de estudio de esta tesis es la Opción Forward Start, específicamente con asignación lineal del precio de strike, para la cual se presentan la replicación de Black-Scholes y la super-replicación bajo una restricción sobre el gamma del portafolio y bajo un modelo subyacente de Movimiento Browniano Geométrico. Bajo la replicación de Black-Scholes, la estrategia de replicación resulta ser una estrategia estática antes de la fecha T' de asignación del precio de strike. Esta tesis muestra que la estrategia de super-replicación bajo la restricción gamma también resulta ser una estrategia estática antes de la fecha T' de asignación del precio de strike. |
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2025 |
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2025-01-29T15:03:10Z |
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2025-01-29T15:03:10Z |
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2025-01-28 |
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Trabajo de grado - Pregrado |
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eng |
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H. Mete Soner, Bruno Bouchard, Ludovic Moreau. Hedging under an expected loss constraint with small transaction costs. HAL, 2016. Myron Scholes, Fischer Black. The pricing of options and corporate liabilities. Journal of Political Economy, 1973. Nizar Touzi, H. Mete Soner. Superreplication under gamma constraints. SIAM: Control and Optimization, 1998. Nizar Touzi, H. Mete Soner. Dynamic programming for stochastic target problems and geometric flows. Journal of the European Mathematical Society, 2002. Nizar Touzi, H. Mete Soner. Stochastic target problems, dynamic programming, and viscosity solutions. SIAM J. Control Optim., 2002. Nizar Touzi, H. Mete Soner. Hedging under gamma constraints by optimal stopping and face-lifting, 2005. Ioannis Karatzas, Jakša Cvitanic. Hedging contingent claims with constrained portfolios. Annals of Applied Probability 3, 1993. Nizar Touzi, Jakša Cvitanic, Huyen Pham. A closed form solution to the problem of superreplication under transaction costs, 1998. H. Mete Soner, Mark Broadie, Jakša Cvitanic. Optimal replication of contingent claims under portfolio constraints. Review of Financial Studies, 1996. Robert C. Merton. Theory of rational option pricing. Journal of Political Economy, 1973. Nizar Touzi, Patrick Cheridito, H. Mete Soner. The multi-dimensional super-replication problem under gamma constraints. Annales de L’Institut Henri Poincaré Analyse Non Linéaire, 2005. S. E. Shreve. Stochastic Calculus for Finance II, Continuous-Time Models. Springer Finance, 2nd edition, 2004. |
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http://creativecommons.org/licenses/by-nc-nd/4.0/ |
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67 páginas |
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Universidad de los Andes |
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Matemáticas |
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Facultad de Ciencias |
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Universidad de los Andes |
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Bajo la replicación de Black-Scholes, la estrategia de replicación resulta ser una estrategia estática antes de la fecha T' de asignación del precio de strike. Esta tesis muestra que la estrategia de super-replicación bajo la restricción gamma también resulta ser una estrategia estática antes de la fecha T' de asignación del precio de strike.Pregrado67 páginasapplication/pdfengUniversidad de los AndesMatemáticasFacultad de CienciasDepartamento de MatemáticasAttribution-NonCommercial-NoDerivatives 4.0 Internationalhttp://creativecommons.org/licenses/by-nc-nd/4.0/info:eu-repo/semantics/openAccesshttp://purl.org/coar/access_right/c_abf2Super-replication under gamma constraints: An application to forward start optionsTrabajo de grado - Pregradoinfo:eu-repo/semantics/bachelorThesisinfo:eu-repo/semantics/acceptedVersionhttp://purl.org/coar/resource_type/c_7a1fTexthttp://purl.org/redcol/resource_type/TPDerivadosGammaBlack-ScholesSonerTouziMatemáticasH. Mete Soner, Bruno Bouchard, Ludovic Moreau. Hedging under an expected loss constraint with small transaction costs. HAL, 2016.Myron Scholes, Fischer Black. The pricing of options and corporate liabilities. Journal of Political Economy, 1973.Nizar Touzi, H. Mete Soner. Superreplication under gamma constraints. SIAM: Control and Optimization, 1998.Nizar Touzi, H. Mete Soner. Dynamic programming for stochastic target problems and geometric flows. Journal of the European Mathematical Society, 2002.Nizar Touzi, H. Mete Soner. Stochastic target problems, dynamic programming, and viscosity solutions. SIAM J. Control Optim., 2002.Nizar Touzi, H. Mete Soner. Hedging under gamma constraints by optimal stopping and face-lifting, 2005.Ioannis Karatzas, Jakša Cvitanic. Hedging contingent claims with constrained portfolios. Annals of Applied Probability 3, 1993.Nizar Touzi, Jakša Cvitanic, Huyen Pham. A closed form solution to the problem of superreplication under transaction costs, 1998.H. Mete Soner, Mark Broadie, Jakša Cvitanic. Optimal replication of contingent claims under portfolio constraints. Review of Financial Studies, 1996.Robert C. Merton. Theory of rational option pricing. Journal of Political Economy, 1973.Nizar Touzi, Patrick Cheridito, H. Mete Soner. The multi-dimensional super-replication problem under gamma constraints. Annales de L’Institut Henri Poincaré Analyse Non Linéaire, 2005.S. E. Shreve. Stochastic Calculus for Finance II, Continuous-Time Models. 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