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Title: Limit theorems and stochastic models for dependence and contagion in financial markets
Author: Granelli, Andrea
ISNI:       0000 0004 6496 1839
Awarding Body: Imperial College London
Current Institution: Imperial College London
Date of Award: 2017
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We analyse the effect of dependence between financial assets in the setting of the variance risk premium and the Brownian semistationary process. The variance risk premium (VRP) refers to the premium demanded for holding assets whose variance is exposed to stochastic shocks. This thesis identifies a new modelling framework for equity indices and presents for the first time explicit analytical formulas for their VRP in a multivariate stochastic volatility setting, which includes multivariate non-Gaussian Ornstein Uhlenbeck processes and Wishart processes. Moreover, we propose to incorporate contagion within the equity index via a multivariate Hawkes process and find that the resulting dynamics of the VRP represent a convincing alternative to the models studied in the literature up to date. The Brownian semistationary process (BSS) is in general not a semimartingale and its univariate asymptotic limit theory outside the semimartingale framework has been developed over recent years, due to the increasing number of its applications in finance and also in the modelling of turbulence. We expand the reach of the theory by proving new probabilistic limit theorems for the 2-dimensional version of the process, using techniques from Malliavin calculus.
Supervisor: Veraart, Almut ; Crisan, Dan Sponsor: Imperial College London
Qualification Name: Thesis (Ph.D.) Qualification Level: Doctoral