  Recent financial disasters have emphasised the need to accurately predict
extreme financial losses and their consequences for the institutions belonging
to a given financial market. The ability of econometric models to predict
extreme events strongly relies on their flexibility to account for the highly
nonlinear and asymmetric dependence observed in financial returns. We develop a
new class of flexible Copula models where the evolution of the dependence
parameters follow a Markov-Switching Generalised Autoregressive Score (SGASC)
dynamics. Maximum Likelihood estimation is consistently performed using the
Inference Functions for Margins (IFM) approach and a version of the
Expectation-Maximisation (EM) algorithm specifically tailored to this class of
models. The SGASC models are then used to estimate the Conditional
Value-at-Risk (CoVaR), which is defined as the VaR of a given asset conditional
on another asset (or portfolio) being in financial distress, and the
Conditional Expected Shortfall (CoES). Our empirical investigation shows that
the proposed SGASC models are able to explain and predict the systemic risk
contribution of several European countries. Moreover, we also find that the
SGASC models outperform competitors using several CoVaR backtesting procedures.
