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Systemic Risk Surveillance

Timo Dimitriadis, Yannick Hoga

TL;DR

This paper tackles the problem of online systemic risk forecast evaluation by introducing time-uniform surveillance schemes for CoVaR, RCoVaR, and related measures that monitor multiple series simultaneously with finite-sample size control. Leveraging strict identification functions and Monte Carlo calibration under the null, the authors derive detectors that jointly test VaR and CoVaR forecasts while enabling attribution to specific institutions via a Bonferroni-type correction. The methodology is validated through extensive simulations on a DCC--GARCH data-generating process, showing accurate size control and substantive power gains, especially for the RCoVaR/CoES/MES families. An empirical application to US banks across multiple crises demonstrates the practical usefulness of online monitoring for regulators and financial institutions, with evidence that more flexible dependence structures (DCC--GARCH) improve systemic risk forecasting during turbulent periods. These contributions facilitate timely countermeasures against distress and advance risk-management practices beyond traditional one-shot backtests by delivering non-asymptotic guarantees and multivariate diagnostic capabilities.

Abstract

Following several episodes of financial market turmoil in recent decades, changes in systemic risk have drawn growing attention. Therefore, we propose surveillance schemes for systemic risk, which allow to detect misspecified systemic risk forecasts in an "online" fashion. This enables daily monitoring of the forecasts while controlling for the accumulation of false test rejections. Such online schemes are vital in taking timely countermeasures to avoid financial distress. Our monitoring procedures allow multiple series at once to be monitored, thus increasing the likelihood and the speed at which early signs of trouble may be picked up. The tests hold size by construction, such that the null of correct systemic risk assessments is only rejected during the monitoring period with (at most) a pre-specified probability. Monte Carlo simulations illustrate the good finite-sample properties of our procedures. An empirical application to US banks during multiple crises demonstrates the usefulness of our surveillance schemes for both regulators and financial institutions.

Systemic Risk Surveillance

TL;DR

This paper tackles the problem of online systemic risk forecast evaluation by introducing time-uniform surveillance schemes for CoVaR, RCoVaR, and related measures that monitor multiple series simultaneously with finite-sample size control. Leveraging strict identification functions and Monte Carlo calibration under the null, the authors derive detectors that jointly test VaR and CoVaR forecasts while enabling attribution to specific institutions via a Bonferroni-type correction. The methodology is validated through extensive simulations on a DCC--GARCH data-generating process, showing accurate size control and substantive power gains, especially for the RCoVaR/CoES/MES families. An empirical application to US banks across multiple crises demonstrates the practical usefulness of online monitoring for regulators and financial institutions, with evidence that more flexible dependence structures (DCC--GARCH) improve systemic risk forecasting during turbulent periods. These contributions facilitate timely countermeasures against distress and advance risk-management practices beyond traditional one-shot backtests by delivering non-asymptotic guarantees and multivariate diagnostic capabilities.

Abstract

Following several episodes of financial market turmoil in recent decades, changes in systemic risk have drawn growing attention. Therefore, we propose surveillance schemes for systemic risk, which allow to detect misspecified systemic risk forecasts in an "online" fashion. This enables daily monitoring of the forecasts while controlling for the accumulation of false test rejections. Such online schemes are vital in taking timely countermeasures to avoid financial distress. Our monitoring procedures allow multiple series at once to be monitored, thus increasing the likelihood and the speed at which early signs of trouble may be picked up. The tests hold size by construction, such that the null of correct systemic risk assessments is only rejected during the monitoring period with (at most) a pre-specified probability. Monte Carlo simulations illustrate the good finite-sample properties of our procedures. An empirical application to US banks during multiple crises demonstrates the usefulness of our surveillance schemes for both regulators and financial institutions.
Paper Structure (19 sections, 7 theorems, 44 equations, 9 figures, 3 tables, 3 algorithms)

This paper contains 19 sections, 7 theorems, 44 equations, 9 figures, 3 tables, 3 algorithms.

Table of Contents

  1. Motivation
  2. Systemic Risk Monitoring
  3. Defining Systemic Risk Measures
  4. CoVaR Monitoring
  5. CoVaR Monitoring with Reversed Conditioning
  6. Simulations
  7. The DCC--GARCH Data-Generating Process
  8. Systemic Risk Forecasts from DCC--GARCH Models
  9. Simulation Results under the Null Hypothesis
  10. Simulation Results under the Alternative Hypothesis
  11. Empirical Application
  12. Conclusion
  13. Proofs of the main paper
  14. The CoES and MES
  15. Defining CoES and MES
  16. ...and 4 more sections

Key Result

Proposition 1

Under $H_0^{\operatorname{CoVaR}}$, it holds for all $k \in [K]$ that where $U_{it}\overset{IID}{\sim}\mathcal{U}[0,1]$ are independent of each other for $i=1,2$ and all $t \in \mathbb{N}$.

Figures (9)

  • Figure 1: Illustration of the Monitoring Windows.
  • Figure 2: Rejection rates of our CoVaR and RCoVaR surveillance methods plotted against the break point in \ref{['eqn:SimParamMisspec']} in the left panel and against the post-break DCC parameter in the right panel. In both plots, we consider $\alpha = \beta \in \{0.9, 0.95\}$ as well as $K \in \{1,2,5,10\}$ for the CoVaR and $K \in \{2,5,10\}$ for the RCoVaR.
  • Figure 3: Rejection rates of the joint CoVaR and RCoVaR procedure in black, and frequencies how often the individual detectors are the first to generate a detection in colors in the setting of the left panel of Figure \ref{['fig:PowerCoVaR']}. Dashed lines depict "first" rejection rates for the VaR detector, and dot-dashed lines for the systemic risk detectors. The colors indicate the respective component of $\bm W_t$. The nominal level of $\iota = 10\%$ is indicated by the dashed horizontal line.
  • Figure 4: Rejection rates of our CoVaR and RCoVaR surveillance methods plotted against the break point for different estimation window lengths $E$, where $E = \infty$ implies the use of the correct parameters. We consider $K \in \{1,2,5,10\}$ and note that the rejection rates of CoVaR and RCoVaR coincide for $K=1$. We further keep $n=1000$, $t^\ast = 0$, $\beta_\text{post} = 0.85$ and $\alpha = \beta = 0.9$ fixed.
  • Figure 5: Normalized VaR and CoVaR detector values for the SPF, and the financial institutions BAC, C, GS, JPM and WFC for forecasts from a Gaussian CCC--GARCH and a Student's $t$ DCC--GARCH model. We use the specifications $\iota=0.1$, $\alpha=\beta=0.95$, $E = 1500$, $n=1000$ and $m=250$. The displayed detector values are normalized by their respective critical values, such that a detector exceeding the black horizontal unit line implies a detection. The vertical dotted lines represent the bankruptcy of Lehman Brothers on 15 September 2008, the beginning of the COVID crisis on 13 March 2020 (when the US declared a national emergency), the collapse of the Silicon Valley Bank on 10 March 2023, and the tariff announcement of Donald Trump on 2 April 2025.
  • ...and 4 more figures

Theorems & Definitions (11)

  • Proposition 1
  • Remark 1: VaR monitoring for the CoVaR
  • Theorem 1
  • Remark 2: Flexibility of detector specification
  • Proposition 2
  • Theorem 2
  • Remark 3: Model-estimation error
  • Proposition 3
  • Proposition 4
  • Theorem 3
  • ...and 1 more