Dynamic CoVaR Modeling and Estimation

TL;DR

This paper develops joint dynamic models for VaR and CoVaR, introduces a new estimation method, and demonstrates improved forecasting accuracy for systemic risk in US banks.

Contribution

It proposes a novel two-step M-estimator for joint VaR and CoVaR modeling with proven statistical properties and applies it to real bank data showing superior forecast performance.

Findings

CoCAViaR models outperform benchmark models in CoVaR prediction.

The proposed estimator is consistent and asymptotically normal.

Finite-sample simulations confirm estimator reliability.

Abstract

The popular systemic risk measure CoVaR (conditional Value-at-Risk) and its variants are widely used in economics and finance. In this article, we propose joint dynamic forecasting models for the Value-at-Risk (VaR) and CoVaR. The CoVaR version we consider is defined as a large quantile of one variable (e.g., losses in the financial system) conditional on some other variable (e.g., losses in a bank's shares) being in distress. We introduce a two-step M-estimator for the model parameters drawing on recently proposed bivariate scoring functions for the pair (VaR, CoVaR). We prove consistency and asymptotic normality of our parameter estimator and analyze its finite-sample properties in simulations. Finally, we apply a specific subclass of our dynamic forecasting models, which we call CoCAViaR models, to log-returns of large US banks. A formal forecast comparison shows that our CoCAViaR models generate CoVaR predictions which are superior to forecasts issued from current benchmark models.