Essays in Multivariate Modelling in Finance
Modelling the dependence structure of financial variables is of paramount importance for a wide range of financial applications. Financial variables exhibit various forms of dependence and tail dependence whereas the magnitude of dependence is not constant over time but rather time-varying and can also be affected by exogenous factors. The present thesis investigates the effects of multivariate dependence on a broad range of financial applications. In particular, the first empirical part of the thesis investigates the implications of dependence and tail dependence for the accurate risk modelling of financial portfolios. The joint behaviour of the returns of the financial portfolios is modelled employing extreme value theory methods for the univariate distributions and pair-copula constructions for describing the joint dependence. The results indicate that risk estimates, derived within this framework, can be successfully forecasted at extreme quantiles. The second empirical part deals with the estimation of systemic risk in the European banking sector based on the CoVaR methodology. In this part, a new methodology, based on copula functions, is proposed and extended to different CoVaR definitions and systemic risk measures. The proposed approach also recognises the time-varying dependence of financial variables by allowing the dependence parameters to be functions of lagged information. The results highlight the importance of taking into account accurate specifications for the marginal distributions and the dependence structure when modelling systemic risk. The empirical results also show that systemic risk in the European banking sector can be explained by several macroeconomic and financial variables as well as factors directly related to institution-specific characteristics. Finally, the third empirical part focuses on the modelling of the interdependence structure of European sovereign yield curves as functions of market-wide and country-specific liquidity and credit quality measures. The empirical results highlight the significance of both liquidity and credit measures in explaining the dynamics and covariation of European yields and reveal important contagion and spillover effects among European economies. Overall, the empirical findings of this thesis outline the importance of taking into account the behaviour and the distribution characteristics of the financial variables that are modelled; failure to do so may lead to incorrect inference and erroneous implications.
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