  CoVaR (conditional value-at-risk) is a crucial measure for assessing
financial systemic risk, which is defined as a conditional quantile of a random
variable, conditioned on other random variables reaching specific quantiles. It
enables the measurement of risk associated with a particular node in financial
networks, taking into account the simultaneous influence of risks from multiple
correlated nodes. However, estimating CoVaR presents challenges due to the
unobservability of the multivariate-quantiles condition. To address the
challenges, we propose a two-step nonparametric estimation approach based on
Monte-Carlo simulation data. In the first step, we estimate the unobservable
multivariate-quantiles using order statistics. In the second step, we employ a
kernel method to estimate the conditional quantile conditional on the order
statistics. We establish the consistency and asymptotic normality of the
two-step estimator, along with a bandwidth selection method. The results
demonstrate that, under a mild restriction on the bandwidth, the estimation
error arising from the first step can be ignored. Consequently, the asymptotic
results depend solely on the estimation error of the second step, as if the
multivariate-quantiles in the condition were observable. Numerical experiments
demonstrate the favorable performance of the two-step estimator.
