Modeling and backtesting systemic risk measures: the case of CoES

Systemic risk has drawn the attention of many researchers and financial institutions since the recent financial crisis. In this article, we first introduce an easy-to-implement and robust multivariate filtered historical simulation (M-FHS) approach to modeling systemic risk measures. We then develop two types of backtesting procedures for CoES, one for CoES alone and one for (VaR,CoVaR,CoES) jointly. We further establish the asymptotic properties of the tests in the presence of the parameter estimation effect. Some Monte Carlo simulations confirm our asymptotic theories and verify the robustness of the M-FHS method. In some empirical applications to large U.S. financial firms, we find that: the backtests for CoES alone behave well when there are some abrupt changes in the systemic risk, like the recent financial crisis, while the joint backtests show their merits when there are some significant changes in VaR but not in CoES; during the financial crisis, the M-FHS method is more responsive to the extreme events than other methods and CoES is more responsive to extreme events than CoVaR. Our M-FHS method, along with two novel backtests, offers financial institutions and regulators a robust and responsive toolset for modeling and evaluating systemic risk.