PhD thesis: “Rough Volatility Modeling in Financial Data Analysis”.

Abstract

This thesis presents four research papers inspired by the rough volatility literature and contributing to it to varying degrees. The first three chapters follow a common thread by introducing the multivariate fractional Ornstein-Uhlenbeck process and applying it to volatility and brain-activity time series modelling. The main properties of the process are analyzed and discussed, and several estimation methods are proposed. The application of the model to volatility time series provides evidence that rough processes effectively capture volatility dynamics and allows us to study the presence of spillover effects in global volatility, documenting asymmetric lead-lag relationships. Applying the same framework to neuroimaging data, we can provide empirical evidence for the integration/orchestration theory in neuroscience by identifying brain regions that act as transmitters and receivers of information. Finally, the last chapter consists of a large-scale calibration study of mixed Bergomi models to VIX implied volatility surfaces that leverages the aid of neural network approximations of the pricing functions.

Examination Committee: Professor Markus Bibinger (University of Würzburg), Professor Florian Bourgey (Quantitative researcher at Bloomberg L.P.), Professor Paolo Pigato (University of Rome Tor Vergata).