  The global financial crisis of 2007-2009 highlighted the crucial role
systemic risk plays in ensuring stability of financial markets. Accurate
assessment of systemic risk would enable regulators to introduce suitable
policies to mitigate the risk as well as allow individual institutions to
monitor their vulnerability to market movements. One popular measure of
systemic risk is the conditional value-at-risk (CoVaR), proposed in Adrian and
Brunnermeier (2011). We develop a methodology to estimate CoVaR
semi-parametrically within the framework of multivariate extreme value theory.
According to its definition, CoVaR can be viewed as a high quantile of the
conditional distribution of one institution's (or the financial system)
potential loss, where the conditioning event corresponds to having large losses
in the financial system (or the given financial institution). We relate this
conditional distribution to the tail dependence function between the system and
the institution, then use parametric modelling of the tail dependence function
to address data sparsity in the joint tail regions. We prove consistency of the
proposed estimator, and illustrate its performance via simulation studies and a
real data example.
