Vives i Santa Eulàlia, Josep, 1963-Díaz Lozano, Pere2023-09-202023-09-202023-06-28https://hdl.handle.net/2445/202102Treballs 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.84 p.application/pdfengcc by-nc-nd (c) Pere Díaz Lozano, 2023http://creativecommons.org/licenses/by-nc-nd/3.0/es/Processos estocàsticsOpcions (Finances)Treballs de fi de màsterStochastic processesOptions (Finance)Master's thesisinfo:eu-repo/semantics/masterThesisinfo:eu-repo/semantics/openAccess