CoVaR: A Measure of Systemic Risk

Moreover, the ΔCoVaR proposed by Adrian and Brunnermeier (2016) provides a measure of the systemic importance of a financial institution. In fact, it compares the conditional financial system losses to a financial institution being in distress by the conditional financial system losses to a financial institution being in its median state.

CoVaR captures the increase in CoVaR when the conditioning event is shifted from the median return of institution i to the adverse VaRi q (with equality).

CoVaR measures the “tail dependence” between two random variables. thus, we note that for jointly distributed random variables, ∆CoVaR is related to the correlation coefficient, while CoVaR corresponds to conditional variance. The conditioning itself decreases the variance, while the conditioning on adverse events increases the expected losses.

Furthermore, the ΔCoVaR studies the increase in CoVaR as a change in the conditioning event related to the performance of an institution i from a normal state to a distressed state.

The ΔCoVaR measure was not only related to an earlier systemic risk literature but also is related to the literature based on contagion and spillover volatility (see Claessens and Forbes (2001)).

On the other hand, the 〖 ∆CoVaR〗^i measures tail dependence and captures common spillovers and exposure effects. In other words, it measures the contribution of an institution i to the systemic risk of the financial system. this contribution can be direct through contractual links between financial institutions or also indirect.

The concept of ΔCoVaR has been well explained, now we focus on the method of estimation of this measure. The ΔCoVaR can be estimated in various ways.

According to Adrian and Brunnermeier (2016) the main estimation method of Δ CoVaR is the quantile regressions method.

This method is used to estimate conditional models to estimate the relationship between a set of independent variables and specific quantiles of the dependent variable.

According to these same authors, there are two ways to estimate the ΔCoVaR; one assumes that the ΔCoVaR is constant over time and the other assumes that it is variable over time.

We start with the first method. We apply the same approach proposed for is estimated CoVaR (previous section), in order to obtain the estimate of this