CoVaR with volatility clustering, heavy tails and non-linear dependence

TL;DR

This paper develops advanced multivariate models incorporating heavy tails, skewness, and volatility clustering to improve the estimation of CoVaR, a key systemic risk measure, and compares their performance through backtesting on European bank data.

Contribution

It introduces a comprehensive framework for CoVaR estimation using non-Gaussian models and copulas, capturing stylized facts of financial returns, and evaluates their effectiveness empirically.

Findings

Models with non-Gaussian features outperform Gaussian models in backtesting.

Copula-based models provide better risk estimates during financial crises.

Volatility clustering significantly impacts CoVaR accuracy.

Abstract

In this paper we estimate the conditional value-at-risk by fitting different multivariate parametric models capturing some stylized facts about multivariate financial time series of equity returns: heavy tails, negative skew, asymmetric dependence, and volatility clustering. While the volatility clustering effect is got by AR-GARCH dynamics of the GJR type, the other stylized facts are captured through non-Gaussian multivariate models and copula functions. The CoVaR$^{\leq}$ is computed on the basis on the multivariate normal model, the multivariate normal tempered stable (MNTS) model, the multivariate generalized hyperbolic model (MGH) and four possible copula functions. These risk measure estimates are compared to the CoVaR$^{=}$ based on the multivariate normal GARCH model. The comparison is conducted by backtesting the competitor models over the time span from January 2007 to March 2020. In the empirical study we consider a sample of listed banks of the euro area belonging to the main or to the additional global systemically important banks (GSIBs) assessment sample.