  Recent financial disasters emphasised the need to investigate the consequence
associated with the tail co-movements among institutions; episodes of contagion
are frequently observed and increase the probability of large losses affecting
market participants' risk capital. Commonly used risk management tools fail to
account for potential spillover effects among institutions because they provide
individual risk assessment. We contribute to analyse the interdependence
effects of extreme events providing an estimation tool for evaluating the
Conditional Value-at-Risk (CoVaR) defined as the Value-at-Risk of an
institution conditioned on another institution being under distress. In
particular, our approach relies on Bayesian quantile regression framework. We
propose a Markov chain Monte Carlo algorithm exploiting the Asymmetric Laplace
distribution and its representation as a location-scale mixture of Normals.
Moreover, since risk measures are usually evaluated on time series data and
returns typically change over time, we extend the CoVaR model to account for
the dynamics of the tail behaviour. Application on U.S. companies belonging to
different sectors of the Standard and Poor's Composite Index (S&P500) is
considered to evaluate the marginal contribution to the overall systemic risk
of each individual institution
