Probability equivalent level for CoVaR and VaR in bivariate Student-\textit{t} copulas with application to foreign exchange risk monitoring

Abstract

We extend the "probability-equivalent level of VaR and CoVaR" (PELCoV) methodology to accommodate bivariate risks modeled by a Student-t copula, relaxing the strong dependence assumptions of earlier approaches and enhancing the framework's ability to capture tail dependence and asymmetric co-movements. While the theoretical results are developed in a static setting, we implement them dynamically to track evolving risk spillovers over time. We illustrate the practical relevance of our approach through an application to the foreign exchange market, monitoring the USD/GBP exchange rate with the USD/EUR series as an auxiliary early warning indicator over the period 1999-2024. Our results highlight the potential of the extended PELCoV framework to detect early signs of risk underestimation during periods of financial stress.