Systemic risk among China's financial sectors: Novel evidence from trivariate CoVaR based on vine copulas

The purpose of this paper is to extend the measure of systemic risk by introducing a trivariate CoVaR that accounts for tail dependence and one-to-many risk spillovers. Unlike the traditional bivariate CoVaR, which captures only one-to-one systemic risk, the proposed measure distinguishes between trivariate upside and downside CoVaRs, integrating risk measurement, tail dependence, and spillover effects within a unified framework. First, we derive the analytical expressions for the trivariate CoVaR using vine copulas, demonstrating that it generalizes the bivariate CoVaR. We further show that ignoring tail dependence leads to overestimating systemic risk in traditional bivariate CoVaR. We construct a vine copula-based trivariate CoVaR model and perform numerical simulations, which confirm its effectiveness in capturing one-to-many risk spillovers while enhancing out-of-sample stability. Finally, we conduct an empirical analysis of systemic risk in China's banking, securities, and insurance sectors, covering the period from January 2007 to December 2024. Our findings indicate that (1) the trivariate CoVaRs of the insurance sector to the banking and securities sectors exceed its own VaRs but remain lower than the bivariate CoVaRs, emphasizing the importance of cross-sector risk spillovers and (2) the trivariate CoVaRs of the insurance sector remain stable across financial cycles, reflecting the risksharing, and return-sharing characteristics of China's financial system. These findings underscore the necessity for financial institutions and regulators to consider cross-sector dependencies when assessing systemic risk.