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tfg_díaz_lozano_pere.pdf (6.51 MB)

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Master thesis

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2023-06-28

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cc by-nc-nd (c) Pere Díaz Lozano, 2023
Please use this identifier to cite or link to this item: https://hdl.handle.net/2445/202102

Rough volatility models using the signature transform: theory and calibration

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[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.

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

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Processos estocàstics, Opcions (Finances), Treballs de fi de màster

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Stochastic processes, Options (Finance), Master's thesis

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Màster Oficial - Matemàtica Avançada

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DÍAZ LOZANO, Pere. Rough volatility models using the signature transform: theory and calibration. [consulted: 9 of October of 2026]. Available at: https://hdl.handle.net/2445/202102

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