Limit theorems and stochastic models for dependence and contagion in financial markets
File(s)
Author(s)
Granelli, Andrea
Type
Thesis
Abstract
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.
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.
Version
Open Access
Date Issued
2016-10
Date Awarded
2017-02
Copyright Statement
Attribution NoDerivatives 4.0 International Licence (CC BY-ND)
Advisor
Veraart, Almut
Crisan, Dan
Sponsor
Imperial College London
Publisher Department
Mathematics
Publisher Institution
Imperial College London
Qualification Level
Doctoral
Qualification Name
Doctor of Philosophy (PhD)