An accurate assessment of tail dependencies of financial returns is key for risk management and portfolio allocation. In the present research project, we will consider a multiple linear quantile regression setting for joint prediction of tail risk measures, namely Value at Risk and Expected Shortfall, using a generalization of the Multivariate Asymmetric Laplace distribution. The proposed method permits simultaneous modelling of multiple conditional quantiles of a multivariate response variable and allows to study the dependence structure among financial assets at different quantile levels. Subsequently, we will introduce an original method for portfolio construction where we derive analytically the portfolio returns¿ distribution from the multivariate structure of the problem. An empirical application to financial returns will be considered to illustrate the practical applicability and relevance of joint estimation of VaR and ES in a multivariate framework.
The recent global financial crisis has demonstrated the importance of measuring the inter-connectivity among institutions. The sudden and uncontrolled breakdown of financial companies not only affects other institutions' health and endangers the stability of the global financial sector, but also has a great impact on the real economy. Large interconnected systems experience fast propagation of shocks from individual institutions to the whole market, emphasising the problem of evaluating the interconnection among institutions. These reasons motivate this research project whose aim is to propose statistical and econometric tools, models and methods to explore and assess extreme risks and tail dependencies among interconnected institutions in a dynamically evolving environment. As a consequence, the introduction of a new modelling framework in risk management, improving existing practises to account for the correlation structure among market participants, undoubtedly represents an important part of this research project. Multiple risks assessment using financial data, necessarily requires the development of a multivariate model-based approach to account for the dynamic evolution of tail risk interdependence. Indeed, tackling the problem from a multivariate standpoint will permit to borrow information across responses and conduct joint inference at the marginal quantiles level, revealing some possible underlying truth that cannot be detected by univariate models. Moreover, from a more practical perspective, this methodology will provide a deeper investigation of the interdependences among multiple financial assets at different quantile levels which may help to detect frequent episodes of contagion and interdependence among institutions which are exacerbated during periods of pronounced volatility on financial markets. In this way tail dependency can be located and consequently be targeted by investment strategies. Eventually, the simultaneous estimation of VaR and ES in one step may be appealing in terms of estimation and efficiency providing risk managers analytical tools and complementary information about rare adverse events that can improve monitoring, forecasting and investment decisions support.