Systemic Risk & Rolling Delta CoVaR

Overview

This project implemented a rolling Delta CoVaR procedure in MATLAB for estimating the contribution of individual financial institutions to systemic risk.

The model follows the CoVaR logic: systemic risk is measured by the conditional value-at-risk of the financial system when a given institution is in distress, and the institution's marginal contribution is measured relative to its median state.

The key implementation contribution was extending the static Delta CoVaR logic into a rolling estimation framework, so that systemic-risk contributions could be tracked over time across multiple institutions.

Problem

Traditional risk metrics often focus on the standalone risk of a financial institution. Systemic-risk analysis asks a different question: how much does the system become exposed when a specific institution enters a distress state?

The goal was to estimate time-varying systemic-risk contributions using institution-level returns, system returns and lagged state variables.

Model Idea

The Delta CoVaR measure compares two conditional states:

CoVaR(system | institution in distress)
-
CoVaR(system | institution in median state)

Institutional distress was estimated through quantile regression at the lower tail, while the normal benchmark was estimated at the median. The system's conditional tail response was then estimated by regressing system returns on the institution's returns and lagged state variables.

Rolling Estimation

The implemented procedure recalculated Delta CoVaR over time. For each institution, the model used expanding or rolling historical windows, estimated the relevant quantile-regression equations and updated the institution's systemic-risk contribution at regular steps.

for each institution:
  for each estimation date:
    estimate median state of institution
    estimate distress state of institution
    estimate system tail regression
    compute rolling Delta CoVaR

This made it possible to inspect whether each institution's contribution to systemic risk was stable, increasing or concentrated during stress periods.

Implemented Elements

• MATLAB implementation of rolling Delta CoVaR calculation.
• Quantile regression for median and distress-state estimation.
• Institution-by-institution systemic-risk contribution estimates.
• Use of lagged state variables as conditioning information.
• Rolling updates across the sample rather than a single static estimate.
• Matrix output of time-varying Delta CoVaR values.
• Comparison between institution distress state and median benchmark state.

Technical Logic

The rolling procedure first estimated the institution's median state:

institution_return = alpha + beta * lagged_state_variables
quantile = 0.50

It then estimated the institution's distress state:

institution_return = alpha + beta * lagged_state_variables
quantile = 0.05

Finally, it estimated the system's conditional tail behavior:

system_return =
  alpha
  + gamma * institution_return
  + beta * lagged_state_variables

Delta CoVaR was computed from the difference between the institution's distress and median states, scaled by the system regression coefficient on the institution.

Outputs

The model produced rolling Delta CoVaR estimates for multiple institutions, allowing comparison of systemic-risk contributions through time.

The output can be interpreted as a time-varying systemic-risk diagnostic: it does not say only which institution is risky in isolation, but which institution is associated with larger deterioration in the system's lower-tail state.

Evaluation Limits

Delta CoVaR is sensitive to modeling choices and should be interpreted as a systemic-risk indicator rather than as a complete causal measure of contagion.

• Quantile choice: results depend on the selected distress threshold.
• Window design: rolling estimates depend on window length and update frequency.
• State variables: omitted conditioning variables can affect estimated contributions.
• Tail estimation: lower-tail regressions can be unstable in small samples.
• Causality: CoVaR captures conditional tail association, not automatic causal transmission.

Modern Extension

A modern version of the project would turn the procedure into a reusable systemic-risk module and expand the validation framework.

• Compare rolling-window and expanding-window estimates.
• Add bootstrap confidence intervals for Delta CoVaR paths.
• Compare CoVaR with marginal expected shortfall and systemic expected shortfall.
• Run robustness checks across quantiles, state variables and stress periods.
• Port the implementation to Python with reproducible notebooks and tests.
• Visualize institution rankings and time-varying risk contributions.

Technologies and Methods Used

• MATLAB for implementation and matrix-based computation.
• Quantile regression for tail and median-state estimation.
• Delta CoVaR for institutional systemic-risk contribution measurement.
• Rolling-window estimation for time-varying risk diagnostics.
• Financial returns for institution and system-level risk inputs.
• Lagged state variables for conditional systemic-risk modeling.

Resources

Code and raw financial data are not public.

An anonymized technical note can be prepared upon request.

Technical Context

• Adrian and Brunnermeier's CoVaR framework for systemic-risk measurement.
• Quantile regression for conditional tail-risk estimation.
• Systemic-risk analytics literature on financial institutions and tail dependence.