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. Popular systemic risk measures include CoVaR, CoES, MES and SRISK etc. However, there are only a few methods available on modeling these measures, and even less papers on evaluating (backtesting) these models. In this paper we first propose an easy-to-implement and robust multivariate filtered historical simulation (M-FHS) approach to modeling systemic risk measures. We then develop a rigorous backtesting procedure for CoES and establish the asymptotic properties of the backtests. Some Monte Carlo simulations confirm our asymptotic theories and verify the robustness of our M-FHS method. In an empirical application to large U.S. financial firms, we find that: compared with competing methods, our M-FHS method is most responsive to the extreme events during the financial crisis, and also most robust to model risk; CoES is more responsive to extreme events than CoVaR