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Rough volatility models using the signature transform: theory and calibration

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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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[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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Rough volatility models using the signature transform: theory and calibration