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DC Field | Value | Language |
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dc.contributor.advisor | Vives i Santa Eulàlia, Josep, 1963- | - |
dc.contributor.author | Díaz Lozano, Pere | - |
dc.date.accessioned | 2023-09-20T10:20:38Z | - |
dc.date.available | 2023-09-20T10:20:38Z | - |
dc.date.issued | 2023-06-28 | - |
dc.identifier.uri | http://hdl.handle.net/2445/202102 | - |
dc.description | Treballs finals del Màster en Matemàtica Avançada, Facultat de Matemàtiques, Universitat de Barcelona: Curs: 2022-2023. Director: Josep Vives i Santa Eulàlia | ca |
dc.description.abstract | [en] In this thesis we study a general stochastic volatility model where the dynamics of the volatility process are described by using the signature transform, a key object in rough path theory which is also very popular in the machine learning community due to its fundamental properties in approximation theory. More specifically, we will present a general model for the evolution of the price of the underlying asset where the dynamics of the volatility are described by linear functions of the (time extended) signature of a primary underlying process. We will finally use this model in practice, showing how it can be efficiently calibrated to market prices of options by a Monte Carlo simulation. | ca |
dc.format.extent | 84 p. | - |
dc.format.mimetype | application/pdf | - |
dc.language.iso | eng | ca |
dc.rights | cc by-nc-nd (c) Pere Díaz Lozano, 2023 | - |
dc.rights.uri | http://creativecommons.org/licenses/by-nc-nd/3.0/es/ | * |
dc.source | Màster Oficial - Matemàtica Avançada | - |
dc.subject.classification | Processos estocàstics | cat |
dc.subject.classification | Opcions (Finances) | cat |
dc.subject.classification | Treballs de fi de màster | cat |
dc.subject.other | Stochastic processes | eng |
dc.subject.other | Options (Finance) | eng |
dc.subject.other | Master's thesis | eng |
dc.title | Rough volatility models using the signature transform: theory and calibration | ca |
dc.type | info:eu-repo/semantics/masterThesis | ca |
dc.rights.accessRights | info:eu-repo/semantics/openAccess | ca |
Appears in Collections: | Màster Oficial - Matemàtica Avançada |
Files in This Item:
File | Description | Size | Format | |
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tfg_díaz_lozano_pere.pdf | Memòria | 6.66 MB | Adobe PDF | View/Open |
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