Rough volatility models using the signature transform: theory and calibration

Treballs finals del Màster en Matemàtica Avançada, Facultat de Matemàtiques, Universitat de Barcelona: Curs: 2022-2023. Director: Josep Vives i Santa Eulàlia

Bibliographic Details
Author: Díaz Lozano, Pere
Format: master thesis
Publication Date:2023
Country:España
Institution:Universidad de Barcelona
Repository:Dipòsit Digital de la UB
OAI Identifier:oai:diposit.ub.edu:2445/202102
Online Access:https://hdl.handle.net/2445/202102
Access Level:Open access
Keyword:Processos estocàstics
Opcions (Finances)
Treballs de fi de màster
Stochastic processes
Options (Finance)
Master's thesis
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oai_identifier_str oai:diposit.ub.edu:2445/202102
network_acronym_str ES
network_name_str España
repository_id_str
spelling Rough volatility models using the signature transform: theory and calibrationDíaz Lozano, PereProcessos estocàsticsOpcions (Finances)Treballs de fi de màsterStochastic processesOptions (Finance)Master's thesisTreballs finals del Màster en Matemàtica Avançada, Facultat de Matemàtiques, Universitat de Barcelona: Curs: 2022-2023. Director: Josep Vives i Santa Eulàlia[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.Vives i Santa Eulàlia, Josep, 1963-2023info:eu-repo/semantics/masterThesisapplication/pdfhttps://hdl.handle.net/2445/202102Màster Oficial - Matemàtica Avançadareponame:Dipòsit Digital de la UBinstname:Universidad de BarcelonaIngléscc by-nc-nd (c) Pere Díaz Lozano, 2023http://creativecommons.org/licenses/by-nc-nd/3.0/es/info:eu-repo/semantics/openAccessoai:diposit.ub.edu:2445/2021022026-05-27T06:46:51Z
dc.title.none.fl_str_mv Rough volatility models using the signature transform: theory and calibration
title Rough volatility models using the signature transform: theory and calibration
spellingShingle Rough volatility models using the signature transform: theory and calibration
Díaz Lozano, Pere
Processos estocàstics
Opcions (Finances)
Treballs de fi de màster
Stochastic processes
Options (Finance)
Master's thesis
title_short Rough volatility models using the signature transform: theory and calibration
title_full Rough volatility models using the signature transform: theory and calibration
title_fullStr Rough volatility models using the signature transform: theory and calibration
title_full_unstemmed Rough volatility models using the signature transform: theory and calibration
title_sort Rough volatility models using the signature transform: theory and calibration
dc.creator.none.fl_str_mv Díaz Lozano, Pere
author Díaz Lozano, Pere
author_facet Díaz Lozano, Pere
author_role author
dc.contributor.none.fl_str_mv Vives i Santa Eulàlia, Josep, 1963-
dc.subject.none.fl_str_mv Processos estocàstics
Opcions (Finances)
Treballs de fi de màster
Stochastic processes
Options (Finance)
Master's thesis
topic Processos estocàstics
Opcions (Finances)
Treballs de fi de màster
Stochastic processes
Options (Finance)
Master's thesis
description Treballs finals del Màster en Matemàtica Avançada, Facultat de Matemàtiques, Universitat de Barcelona: Curs: 2022-2023. Director: Josep Vives i Santa Eulàlia
publishDate 2023
dc.date.none.fl_str_mv 2023
dc.type.none.fl_str_mv info:eu-repo/semantics/masterThesis
format masterThesis
dc.identifier.none.fl_str_mv https://hdl.handle.net/2445/202102
url https://hdl.handle.net/2445/202102
dc.language.none.fl_str_mv Inglés
language_invalid_str_mv Inglés
dc.rights.none.fl_str_mv cc by-nc-nd (c) Pere Díaz Lozano, 2023
http://creativecommons.org/licenses/by-nc-nd/3.0/es/
info:eu-repo/semantics/openAccess
rights_invalid_str_mv cc by-nc-nd (c) Pere Díaz Lozano, 2023
http://creativecommons.org/licenses/by-nc-nd/3.0/es/
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/pdf
dc.source.none.fl_str_mv Màster Oficial - Matemàtica Avançada
reponame:Dipòsit Digital de la UB
instname:Universidad de Barcelona
instname_str Universidad de Barcelona
reponame_str Dipòsit Digital de la UB
collection Dipòsit Digital de la UB
repository.name.fl_str_mv
repository.mail.fl_str_mv
_version_ 1869408679970734081
score 15,300719

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