Marginal expected shortfall inference under multivariate regular variation

Marginal Expected Shortfall is widely regarded as an important measure of systemic risk. Its accurate estimation is crucial for assessing the vulnerability of the banking sector to severe financial market downturns and for understanding the potential contribution of individual institutions to system-wide distress. Existing statistical methods typically rely on a bivariate extreme-value framework, which neglects the complex extremal dependence among the many financial institutions that compose the banking sector. In this work, we show that explicitly accounting for dependence substantially improves the accuracy of risk assessment. To this end, we propose an inferential procedure grounded in multivariate regular variation theory. We derive an approximating formula for the extreme marginal expected shortfall, from which we construct both an estimator and a bias-corrected version. Our framework accommodates β-mixing time series with heavy-tailed innovations, covering a wide range of popular models as well as identically distributed data. Within this context, we establish the consistency and asymptotic normality of the proposed estimators, enabling the construction of reliable confidence intervals. Simulation studies demonstrate that the new estimators – especially the bias-corrected version – significantly outperform existing methods, with highly accurate confidence intervals. Finally, an application to financial return data illustrates the practical relevance of the proposed inferential procedure.